Find two unit vectors orthogonal to a=⟨2,-2,-3⟩a=⟨2,-2,-3⟩ and b=⟨3,2,2⟩b=⟨3,2,2⟩ enter your answer so that the first non-zero coordinate of the first vector is positive.

Question

Mathematics

Tania Malone

22 July, 12:17

Find two unit vectors orthogonal to a=⟨2,-2,-3⟩a=⟨2,-2,-3⟩ and b=⟨3,2,2⟩b=⟨3,2,2⟩ enter your answer so that the first non-zero coordinate of the first vector is positive.

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Answers (1)

Know the Answer?

James Jackson · Answer 1

We need the cross product of the two vectors.

a x b

= x

=

i j k

2 - 2 - 3

3 2 2

=

=

The second vector is obtained by reversing the direction, namely

Thus the two vectors are and.