Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned by the vectors (-2, 6) and (3, 6 (Use symbolic notation and fractions where needed. Give your answer in the form (*, *) .) G (u, v) =

Q: Show that the points (5,4,2) ,(6,2,-1) and (8,-2,-7) are collinear

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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 cross product a × b where a = (0, 3, 4) and b = (5,1,2). axb =

A: Step 1: Step 2: Step 3: Step 4:

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

A: topic - vectors

Q: Determine if the vectors , and are linearly independent.

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Q: Find all points that simultaneously lie 3 units from each of the points (2, 0, 0), (0, 2, 0), and…

A: Let such a point is (x,y,z)

Q: Let à = (-5, - 2, 4) and b = (-1,5, 3). Find a x b. (Enter your answer as a vector of the form .)…

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Q: If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates…

A: On solving this we will get:-

Q: Find a linear map 7 that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

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Q: Determine if u = (0,3, -4) and v = (1, -8, -6) are orthogonal, parallel or neither.

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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: Determine whether the points (-6, 5), (1, 7), and (16, 10) are collinear.

A: Given: -6,5, 1,7  and 16,10 Concept Used: Three points are collinear if area of triangle is zero.…

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…