Let u, v and w be the vectors in R given by Write w as a...

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Let u, v and w be the vectors in R³ given by Write w as a linear combination of [1, -2, 7] and [1, -3, 3]. [1, -2, 7] + Enter a vector in R³ as [x, y, zl. W= [1, -3, 3] = u = 5[1, -2, 7] + 1[1,−3, 3], v = = 1[1, -2, 7] – 3[1, -3, 3], and w = 4u + 3v. For v and w€ R³, if ||vw|| = 3, ||v|| = 4 and ||w|| = 6 Then v. w = (Hint: Use the fact that ||v − w||² = (v - w). (vw).) - If is the angle between the vectors v and w, then cos Let proj, w be the projection of w to v. Then (proj, w). v = Let u, v and w be the vectors in R³ given by Write w as a linear combination of [1, -2, 7] and [1, -3, 3]. [1, -2, 7] + Enter a vector in R³ as [x, y, zl. W= [1, -3, 3] = u = 5[1, -2, 7] + 1[1,−3, 3], v = = 1[1, -2, 7] – 3[1, -3, 3], and w = 4u + 3v. For v and w€ R³, if ||vw|| = 3, ||v|| = 4 and ||w|| = 6 Then v. w = (Hint: Use the fact that ||v − w||² = (v - w). (vw).) - If is the angle between the vectors v and w, then cos Let proj, w be the projection of w to v. Then (proj, w). v =

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