Which of the following points is on the xz plane? a) (1, -3, 0) b) (0, 4, 0) c) (0, 3, -2) O d) (2, 0, -3)

Q: 02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A: Please refer the attached image for complete solution.

Q: 1) in triple dot of vectors |(A x B). C = |(CX A). B\, where the vectors A, B, and C are not same…

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Q: b) Show that the points A = (1, 2, 2), B = (3,4, 5) and C = (-1,0, –1) lie on a plane through the…

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Q: Find the angle of intersection of the plane 2x+3y+5z=−32x+3y+5z=−3 with the plane 3x+2y−1z=0

A: Given: - The plane is, 2x+3y+5x=-3, with the plane 3x+2y-z=0 To find: - The angle of intersection of…

Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – z =11 and 4x + 2y – 3z =…

A: We need to find a vector parallel to the line of intersection of the planes 2x+3y-z=11 and 4x + 2y -…

Q: Find a vected that is Perpenditular to the Plane that Contaiins the e poin +s P(2,3,4), Q~2)0,5), R…

A: Given: The three points:  P (1 , 3 , 4 ) , Q ( - 1 , 0 , 5 ) and R ( 4 , 2 , 2 ).   To determine: A…

Q: Verify that the two planes −x + 6y + 2z = 3,   −(1/2)x + 3y + z = 4 are parallel and find the…

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Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in…

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Q: Find the symmetrical point of point P(-1,-3,5) with respect to the plane D:3x-2y+z+6=0

A: Point P(-1,-3,5)  plane D:3x-2y+z+6=0

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

A: In xy plane z = 0 = t - 3. Therefore t = 3 so the point of intersection is (-2,10,0). Similarly.

Q: Are the planes 1/2 x + 2y − z = 5 and 3x + 12y − 6z = 1 parallel?

A: Given: Are the planes 1/2 x + 2y − z = 5 and 3x + 12y − 6z = 1 parallel?

Q: What is the intersection of the plane x+2y+z =0 and the line (x, y,z) = (0,1,2)+ k(–1,1,2), kER?

A: Consider the equation of plane x+2y+z=0 and the equation of line x,y,z=0,1,2+k-1,1,2. Find the…

Q: Verify that the two planes −3x + 6y + 7z = 1 , 6x − 12y − 14z = 25 are parallel and find the…

A: Given equations of two planes are: -3x+6y+7z=1 and, 6x-12y-14z=25 Thus we can define the normal…

Q: Indicate on an xy-plane those points (x, y) for which the statement holds. |x − 3| ≤ 5 and |y + 2|…

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Q: For what positive value of cc is the acute angle between the plane containing the points A(0,0,1),…

A: According to the given information, it is required to find the positive value of c is the acute…

Q: 37 Find the equaton of a plane that contains the point (4, -3, –1) and is perpendicular to the…

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Q: Find the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…

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Q: Find the symmetrical point of point P(1, 3, 4) with respect to the plane D:3x-2y+z+6=0.

A: Symmetrical point at plane problem....

Q: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

A: Let M be a plane that contains the point with coordinates -2, -2, -1 and is orthogonal to the vector…

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: Find an equation of the plane through (-7, 2, –6) that is perpendicular to the planes 4x – y + z = 4…

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Q: Which of the following planes is parallel to the plane 3x – 2y + z= 3? - Oz=3x- 2y + 9 z = 6x- 4y +…

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Q: Find the points of intersection of the line x = 3 + 2t, y = 7 + 8t, z = -2 + t, that is, I(t) = (3 +…

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Q: is ndicular tò the plane containing the points: A = (-1,1, 2) B = (-3, 2, 1) C = (5 – 1, 1) the

A: Given that the plane is passes through the point A, B and C. We have to find the normal vector of…

Q: Evaluate Sf,(z+ 3y – x²) dS where S is the portion of z = 2 – 3y + x² that lies over the triangle in…

A: Ans :

Q: 7. If a =i+ 3j – k, b= 2i+ 4j – 2k and c = -i+2j+ 4k, find a number A such that d= a+b+ Ac is…

A: Given a=i+3j-k b=2i+4j-2k c= -i+2j+4k Find the  λ such that d= a+b+λc is parallel to the yz plane…

Q: Show that the planes given by 2x − 4y − 3z = 5 and −4x + 8y + 6z = 1 are parallel, and find the…

A: Solution:Given2x − 4y − 3z = 5 −4x + 8y + 6z = 1To prove :The planes are parellel and to find the…

Q: Show that the minimum distance from the origin to a point on the plane ax + by + cz = d is |d| Ja? +…

A: Given :               ax + by + cz = d         We know that minimum distance (p) of a point x1,y1,z1…

Q: Find the distance from the point B = (1, 0, 2) to the plane P whose general equation is x + y -z =…

A: Equation of the plane is Given point is

Q: A. Show that the planes (x+ y– z = 1 ) and (2x – 3y+ 4z = 5 ) are neither parallel nor…

A: let the normal vectors for the vectors be a1, a2 thus a1=<1,1,-1> and a2=<2,-3,4>. Let…

Q: r = (6,-3,2)+1(2,0,1) + u(1,1,–3)

A: Given point is (0,-1,-8) and the plane is r→=6,-3,2+t2,0,1+u1,1-3

Q: R) show that the pints ACI,l,4), B(2,2,2), c (o,1,5) and D(1,0,5) are coplanear (in the Same plane).

A: Form the three vectors and take the determinant of them. If determinant equal to zero it means all…

Q: 5. Find a plane through the points P(1,2, 3), P2(3, 2, 1) and perpendicu- lar to the plane 4x – y+…

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Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

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Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with the xy-plane,…

A: Given, The line x = -2,  y = 4+2t ,  z = -3+t   We have to find the points of intersection of line…

Q: Find a plane that contains S and is perpendicular to the plane that contains the points

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Q: choose between Parentheses No. columu unit veetor on the Plane a 4x+22-4y =3 is the Vector %3D O…

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Q: Find a parametrization for the line segment beginning at P, and ending at P2. P (2,-3,2) and P2(0, –…

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Q: Find the value of d in the equation of the plane ax+by+cz+d=0 passing through the point P(3, 1, -2)…

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Q: tor that is norma to the Plane determined by the three Points i+ 2j +k, si-j+ k , 3i + 2; - 7k.

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Q: Determine the distance from point P(-2, –1, 1) to the plane [x, y, z] = [4, –1, 6] + t[1, 6, 3] +…

A: Parametric equation of a plane is: x,y, z=p+at+bs where a and b are the vectors parallel to the…

Q: 7. If a -i+3j – k, b = 2i + 4j– 2k and c = d = a+b+ de is parallel to the yz-plane. -i+ 2j + 4k,…

A: given a=i+3j-kb=2i+4j-2kc=-i+2j+4k

Q: Which of the following vector is perpendicular to the plane 2x - 3y + 5z +7 = 0? O1-6, 1, 3] O [2, -…

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Q: What is the intersection of the plane x+2y+z=0 and the line (x,y,z) = (0,1,2)+ k(-1,1,2), kER?…

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Q: Find the point at which the line 7(t) = +t intersects the xy plane. %3D

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Q: What is the intersection of the plane x+2y-z=0 and the line (x.y,z) = (2,2, - 3)+ k(4,–1,1), kER?…

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Q: Let P be the plane with equation −x+2y−2z = 3. Find four distinct points on P at distance 3√10 to…

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Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane – 6x + 8y – 10z 4 = 0 are in…

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Q: Find the distance of the plane passing through the points ā, b, c from the origin.

A: First we derive the vector equation of plane.    The perpendicular distance is the projection on the…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.