Find the cross product a x b. a = (1, 1, -1), b = (2,7,9) Verify that it is orthogonal to both a and b. (a x b). a = (a x b). b = x X

Q: = Let -3 -1 -~--~--~--~--~- , V3 -5 1 , V₂ 2 0 combination of V₁, V2 and V3. 5 -26 , V4 -9 -1 -3…

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Q: Find the cross product u x v where i = 3i +6j +9k and v = (- 2, – 4, 5). ux v =

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Q: Find the cross product a × b. a = j + 9k,    b = 4i − j + 2k       Verify that it is orthogonal…

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Q: Show that V1, V2, V3 are linearly independent, but V₁, V2, V3, V4 are not. Then express V4 as a…

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Q: Verify that (AB)T = BTAT.

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Q: Let x=x= and y=y= Find the dot product of xx and yy.     x⋅y=x⋅y

A: Given:x=9, 0y=-4, -2Dot product:A=ax ,ay  B=bx ,byAB=axbx,+ay,by

Q: ) Let B = {vi =,₂ =, V3 =}. Determine whether B is linearly independent or linearly dependent.

A: Let us consider a set of vectors V=v1,v2,.......vn. The set of vectors are said to be linearly…

Q: Express the following as a linear combination of u = (6, 1, 7), v = (1, -1, 4) and w = (1, 8, 7).…

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Q: Let ā = (1, 3,-1) and b (-1,0, 2). What is the y-component of ā x b %3D %3D 1 -1 3.

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Q: Find the cross product a x b. a = j + 6k, b = 3i - j + 5k Verify that it is orthogonal to both a and…

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Express w as a linear combination of u and v. 4 --}-}--[:] W = 6 u 3 2 6 6

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Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

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Q: Express the following as a linear combination of u (2, 1, 5), v (1,-1, 4) and w = (6, 8, 6). (9, 14,…

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Q: Write v as a linear combination of u and w, if possible, where u = (2, 1) and w = (2, -2). (Enter…

A: u=2, 1 and  w=2, -2To express v=4, -1 as a linear combination of u and w

Q: v1 =[ 2 5 1 ] , v2 =[ − 3 1 − 1 ] , b =[ 11 19 5 ] Show that b is in Span{v1,v2}. Express b as a…

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Q: Let v = (5, 8) and w = (4, 5). What is the dot product v · w?

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Q: Let ā = (−1, 1, 3) and 6 = (0, -4, k). a Find k so that a and b will be orthogonal. k =

A: k=34​Explanation:   Two vectors are orthogonal if their dot product is zero.   Therefore, k=34​   (…