Verify that the two planes are parallel. -x + 6y + 3z = 6 1 -x + 2y + z = 7 Find the normal vector, n,, to -x + 6y + 3z = 6. n1 1 Find the normal vector, n,, to - + 2y + z = 7. n, = Because n, |n, the planes are parallel. Find the distance between the planes.

Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

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Q: Express the vector == 7= Z+ y. -22] 10 as a linear combination of = -(-3) and y=

A: Consider the vector v→=-2210. To express it as linear combination of vectors x→=-4-5 and y→=1-5.…

Q: Which of the points P = (-1,4,-7) and Q = (6,-1,5) is closest to the z-axis? OQ (6,-1,5) OQ (6,-1,0)…

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Q: Find the cross product x where = 71-7j -4k and 7 = (-4,-3, 4). úxv=

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Q: Find the vector equation of the line that goes through the point (10,15,9)(10,15,9) and is…

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Q: Suppose vector a= (4, -6, 10) and vector B= (-6, 9, -15). What is a x b?

A: topic - vectors

Q: Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, - 1).

A: We have to find a direction vector for the line containing the points -1, 5, 2 and 2, 3, -1. We know…

Q: Perform the indicated operations for the given vectors. r=(4, 7), -(10, -10)..-(1, -6) Find v+s-r…

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Q: Sketch the vectors = (2, 3,-6) and w = (-1,1,1) and draw -U, v + w and 7 - w.

A: The given vectors are

Q: 5. Complete the table with the points of the image by applying the vector (-3, 5). Preimage A (-1,…

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Q: 4x бу Find dA, where R is the parallelogram enclosed by the lines 6x + 2y 0, 4x R 4х — бу - 6y = 4,…

A: Evaluate the double integral by change of variables

Q: Q1(A): 19 Marks] Two vectors A and B are located at Pi(2,2,2) and P2(2,-2,-2). Write vector notation…

A: Two vectors A and B are located at P(2,2,2) and P2(2,-2,-2). Write vector notation for each starting…

Q: You are at the point (3,2,3)(3,2,3), standing upright and facing the xzxz-plane. You walk 4 units…

A: Given: You are at the point (3, 2, 3 ), standing upright and facing the xz-plane. You walk 4 units…