Question

TETETTERE Find u xv. u = (0, 1, -6), v= (1, -1,0) Show that u x v is orthogonal to both u and v. (u X v) · u = (u x v) v = Need Help? Read It Talk to a Tutor Solond Answer with CamScanner

Answer 1

Let, u=ai & bj+ck v=di tej + fk cross product the determinant of ie (a, b, c) and ie ( d, e, f) be two vectors, UX у is defined by then the ci K the matroise b d e f Here u= (0, 1,-6) ie V = (1,-1,0) ie o.lt 1. ) + (-6) k 1.2+(-1).) + OK and 1 к . UxV det O K -6 o 0 tk 10 O [C-606-8) ---6] + K [01-1) – (1-1)] ;[0 +6]+ k[ 0-1 — К. -bi – 67 (-6)i + (-6) j + (-1) UXV f6, -6, -1)

(a, b, c) and Two vectons N=(d,e,f) are said to be orthogonal if u. V where, adt be t of u.V= will be to both u uXV so, orthogonal and v ich and (uxv). V = 0 (uxv). Uzo now, and uxv = (-6, -6, -1) (o 1-6) V= (1,-1,0) u = (ux~). U = (6x0) + (-6) 1 + 616-6) 0-6+6 (uxv). u v=0 And, (uxv). V = x + (-6) (-1)+(-1)*0 -6+6 to (Uxv). V = 0

as well as (uxviv=0 This (uxv). U (ux). U =0 so, luxv) is on thogonal onal to both u and v. (shown) Answers их у= (-6, 6.-1) (Uxw).u To O (uxv), v 17 o