Question

2. Determine a vector that is perpendicular to both a=(5,3,-1) and 5=(4,- 2.7). Show that your newly created vector is perpendicular to both i and 7 4. Solve for x if ū=x,2 x,- 3 x and lūl=21.

Answer 1

Solution 2 ă. (5, 3,-1) B = ( 4,-2,7) Lete be vector perpendicular to both å and b 2 le The vector perpendicular to vector is calculated by Crass of these 2 vectors. ê product I K b c р (PQ, R) one the Where (a, b, c) and 2 veetors Now in this case وع Ts 5 3 -- 1 = (3.7- (-1)(-2))-(3-5- 4.(-1)) ) + ((-2)(5) - 4,3) 4 - 2 7 € ê ( 21-2) - Î ( 35+4) + ß (-10-12) 19 ê - 39 ] - 22 Au verification leeg By Doing dot Product Dot Product must be zero 0 < 19 ê- 399 - 22 F>. <5 h +3î - Ê 2 (95-117 +22) 2 < 19ê - 89 1- 22R>. <4^-29 +78) z (76+70 -154) An

13 (2, 20, 9-30 a) lul = 21 { magnitude) vector is calculated by Magnitude of lül Ja²r y² + z 2 In this case (22) ²+ (22) 21 = 2 of (3x)2 21 N² + 40² +90² 21 = no 4 14 4 + 9 Na 2) J14 N = 3245TL 142 N = 3 y 2 Aux