Question

Find the cross product <–1, –3, –8> × <7, 4, –5>. Is the resulting vector perpendicular to the given vectors?

Answer 1

Answer: <47, -61, 71>; yes

Explanation:

Answer 2

The cross product is 47 i - 61 j + 17 k.

Explanation:

Given that-

a = < -1, -3, -8 > , b = < 7, 4, -5 >

The cross product is

a × b =
`\left[\begin{array}{ccc}i&j&k\\-1&-3&-8\\7&4&-5\end{array}\right]`

= i ( - 3 × -5 - 4 × -8 ) - j ( -1 × -5 - (-8) × 7 ) + k ( -1 × 4 - 7 × -3 )

= i ( 15 + 32 ) -j ×( 5 + 56 ) + k ( -4 + 21 )

= i ( 47) - j (61 ) + k (17)

= 47 i -61 j + 17 k

As we know that if two vectors A & B are perpendicular then

A . B = 0

So here only the given vector b = < 7,4, -5> is perpendicular to the resulting vector .