Are the following statements true or false? Explain why or why not. (a) A vector has only one unit vector parallel to it. (b) There is only one parametrization for a line or line segment. (c) The sphere x2 + y2 + z2 = 1 is a three-dimensional surface. (d) If u + v = w, then ∥u∥ + ∥v∥ = ∥w∥

Q: (a) What equation describes every vector w = (w1, w2) that is perpendicular to v = (-1,-2)? ալ + աշ…

A: This is the complete solution.

Q: Let c be a number, and let a and b be vectors in R³. Let x = (x, y, z). Show that the equation (x−…

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Q: Given a vector and 2 points, A(5,–2,7) and B(9,–2,1) in a plane. (a) Find dot product of vector…

A: A vector is a quantity that has both magnitude and direction. In general, vectors are represented as…

Q: 1. Consider the plane 4x – 3y + z = 6. (a) Which of the following points lie in the plane? i. (1,4,…

A: Plane

Q: 2. a) Find the line of intersection of the two planes. (answer in parametric form) π₁: 4x-5y-2z=1…

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Q: Qestion 2 a). Use vector projection to explain the distance in part (iii) equation b). find the…

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Q: 5. Determine vector and parametric equations of the plane that... a) has the scalar equation 2x-y+…

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Q: i am so confused i dont understand please help thank you

A: Step 1: Step 2: Step 3: Step 4:

Q: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: nts A, B, C, D are positioned such that the line AB is perpendicular to CD, and BC is perpendicular…

A: In the following question, the concept of the dot product is applied. Dot Product The product of the…

Q: OABC is a tetrahedron where O is the origin and A, B and C are the other the →→ ->> ectors a, b and…

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Q: Write a vector and parametric equation of each plane. a) contains the points A(1, 2, - 2), B(3, -9,…

A: (a) A plane contain three points which are,

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A: (a)  The augmented matrix for given system of planes is…

Q: Write the scalar equation of the plane. a) perpendicular to the line [x, y, z]=[1 -2, -3]+t[5, – 4,…

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Q: 5x – 3y – 13 = 0 is a scalar equation for a line in 2-space. a) State 2 points that are on the line.

A: Given: the equation of straight line  5x-3y-13=0                 Answer a) all the points which are…

Q: hine the cartesian equation of the plane th 4), and C(4, 5, 5).

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Q: 1. For the plane passing through points A(1, 5, 9), B(2, -3, -4), and C(1, 4, –1), find a) a vector…

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Q: Q1:A-Find the equation of plane passes through (0,2,-1) parallel to the plane 3x+y+z=7? b- Find…

A: 1. A. According to question,Given plane,3x+y+z=7,Given Point 0, 2, -1

Q: 8. Time to explain: a) why does the vector equation of a plane have two parameters, while the vector…

A: Part (a) A line is a defined in one dimension, whereas, a plane is defined in 2 dimensions. So, for…