Given vectors A=^x2-^y+^z3 and B=^x3-^z2, find a vector C whose magnitude is 9 and whose direction is perpendicular to both A and B.

acapotivigl

acapotivigl

Answered question

2022-09-05

Given vectors A = x ^ 2 y ^ + z ^ 3 and B = x ^ 3 z ^ 2, find a vector C whose magnitude is 9 and whose direction is perpendicular to both A and B.

Answer & Explanation

Ashlee Ramos

Ashlee Ramos

Beginner2022-09-06Added 20 answers

Let C = ai+ bj+ ck
C.A = 0 => 2a-b+3c =0
C.B =0 => 3a-2c =0 => a = 2/3 *c => b = 13/3 *c
Mod C = 9 => a^2 + b^2 +c^2 = 81
(4/9+ 169/9 +1 )c^2 = 81
=> c = (729/182)^.5 =+/- 2
a = +/-1.33
b = +/-8.67
C = +/-(1.33i + 8.67 j + 2k)

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