Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar
A: We can check whether the three vectors are co planar or not as below
Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…
A: We find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q =(4,-2,1)…
Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…
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Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)
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Q: A vector orthogonal to the plane through the points (-1,0, 0), (0, 0,-2), (2, 3, 4) is
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Q: A normal vector for the plane through the points (2, 5, 1), (3,7,0), and (2, 5, 2) is: O (-2, –1,0)…
A: Let the given points in the plane be A(2, 5, 1), B(3, 7, 0), C(2, 5, 2)
Q: Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a rectangular…
A: Question- Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a…
Q: A vector orthogonal to the plane through the points (-1,0,0), (0, -2, -2), (2, 3, 4) is < 2, – 10, 6…
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Q: Show that the vectors ⟨1, 2, 3⟩, ⟨1, 1, 0⟩, and ⟨3, 4, 3⟩ lie in the same plane
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Q: ind a unit vector with positive first coordinate that is orthogonal to the plane through the points
A: Given that the plane passes through the points, P(4,1,-1) Q(5,2,0) R(5,2,5)
Q: 13. Find an equation of the plane through the point (1,2,3) and perpendicular to the vector…
A: Given a point P( x, y, z) and a vector (a, b, c) which is perpendicular to the given plane
Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…
A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…
Q: Find a vector that is orthogonal to the plane containing the points. (Orthogonal means…
A: Given points are, P=3,0,1Q=4,-2,1R=5,3,-1 The orthogonal vector n^ will be calculated from the given…
Q: Find a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…
A: Coordinator of the plane is given Find out the vector that is perpendicular to the plane
Q: 2. Consider the vectors [2, 1, 0, 0], [3, 1,0, 0], [0,0, 0, 1) in R". Find a vector v so that v, (2,…
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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, –2), (2, 3, 4) is
A: Query- Find a vector orthogonal to the plane through the points -1,0,0,0,-2,-2,2,3,4. Answer- Let…
Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…
A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]
Q: Find a vector equation for the line through the point Pla,-1,0,3) that is orthogonl t the hyperplane…
A: Suppose a line passing through the fixed point with position vector a and parallel to vector b, then…
Q: Consider the vectors (2, 1,0, 0), [3, 1,0, 0], [0,0, 0, 1] in R". Find a vector v so that v,…
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Q: Find a nonzero vector orthogonal to the plane through the points P, Q and R if P(1,0,0), Q(7,8,0)…
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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P=(2,0,-4),…
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Q: Find a vector v that is perpendicular to the plane through the points A = (4, – 5, –2), B = (2,3,…
A: We are asked to find the vector that perpendicular to the plane through the points
Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2
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Q: Find the orthogonal projection of the vector (2,4) about the line L parallel to the vector (-1,2)
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Q: Find the vector component of the vector U orthogonal to a: и %3D (4, —1,2) and a %3D (1,3, —2).…
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Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, -4,0), v = (-1,-1,2,2), and…
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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 1, –-2), (2, 3, 4) is O O O O
A: I have append the formula in solution part
Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩
A: I have appended the formula used in the solution part of the question
Q: The terminal point of the vector v = i +2j +3k with initial point (4, 2, –3) is
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Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…
A: Given, The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).
Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…
A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…
Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…
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Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…
A: From the given points we can find two vectors and after that, using the fact that if one vector is…
Q: Show that the column vectors (1,1.2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1.6) vectors in R are…
A: We have to prove that the given Column vectors are linearly dependent in R4.
Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)
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Q: Find a nonzero vector orthogonal to the plane through P(2,5, 1), Q(-3, 1, –2) and R(5, –3, –1).
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Q: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…
A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)
Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…
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Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…
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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 0, -2), (2, 3, 4) is
A: We will solve the problem
Q: Find a nonzero vector orthogonal to the plane through P(2, 5, 1), Q(-3, 1, – 2) and R(5, –3, –1).
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Q: Find two vectors of norm 1 that are orthogonal to the vectors u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2)…
A: Let X=x,y,z,t be the vector that is orthogonal to u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2) and w= (3,…
Q: Find a vector which is orthogonal to the vectors ū = (2, –2, 1) and ū = (4, 3, – 1).
A: Explanation of the answer is as follows
Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1, -2), (2, 3, 4) is
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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is O O O O
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Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³
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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…
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Q: Consider the plane that goes through the point (4, 1, 3) I to vector (2, 3, 1).
A: It is given that the plane is passing through the point (4,1,3) and orthogonal to the vector (2,3,1)…
Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…
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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1,-2), (2,3, 4) is O O O O
A:
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- 5. (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors (1, –3, 2), (2, 1, -3) and (-3, 2, 1) linearly independent?Q1) Find the equation of the plane passing through the point (4,-1,-5) and perpendicular to the vector <1,2,1> ; _x+_y+_z=_Find the equation of a plane passes through (1, 2, 3), (3, 2,1) and (-1, -2, 2) 4x - 3y + 4z = 10 4x + 3y + 4z = 10 4x +3y - 4z = 10 4x - 3y4z = 10
- Which vector equation below represents the line in R³ that passes through the point (-4, 5, 7) and is perpendicular to both a = and b = ? - Or(t) = 4, 5, 7> OF(t) = Or(t) = 4, 5, 7> + t 1 + t Or(t)= 4, 5, 7> + t Or(t) =Find the plane through the points (7,7,5), (1,3,6) and (5,-2,-1)Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line. Point Perpendicular to x-1 (9, 2, 2) *¹ = } 4 = y + 2 = z +9 -9
- The line that passes through the point (4, –2, 0) and parallel to the vector (1, 2, -3) has symmetric equation _. Check all that applies. y + 2 x – 4 = 2 || 3 x – 1 = 4 – 2y, z = -3 6x 24 = 3y + 6 -2z - 1 y – 2 4 E- = z -2Suppose that v1 = (2,1,0,3), v2=(3, 1,5,2), v3 =(-1,0,2,1) are column vectors temporarily lying down Which of the following vectors are in span of (v1,v2,v3) ? (There are multiple correct answers) (2,3, -7,3) (0,0,0,0) (1,1,1,1)Find the vector and parametric equations of the line that passes through the points A(7,10,4), B(3,-2,2)
- Determine the vector equation of a plane that contains the line with symmetric x 3 1 equation *+-+¹_2+2 and the point P(1,3,0). = 5 4 = (1,3,0) + s(-2,5, 4) + t(3, 1,2), 5, € R | 7 = (1,3,0) + s(-2,5,4) + t(4,4,2), s, € R | 7 = (1,3,0) + s(−2,5,4) + t(1,3,0), 5,± € R none of the aboveFind the vector, parametric, and symmetric equations for each of the following lines: (a) the line perpendicular to x+7_y_4 3 -4 with x-intercept -: the line parallel to (x, y, z) = (2, 0, -7)+t(8, -2, 12) with the same y-intercept as 3x + 5y-z = 50: (b)Find the equation of the plane containing the points (0, 1, 3), (2, 2, 2) and (3, 2, 1)