Question

PLEASE HELP. WILL GIVE BRAINLIEST !! Find the cross product <-1, -3, -8> x <7,4, -5>. Is the resulting vector perpendicular to the given vectors?
<47, -61, 71>; yes
<41, -59, 77>; no
<-59, 71, 41>; yes
<41, -61, -59>; no

Answer 1

Answer:

Answer:

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

Step-by-step explanation:

Given that-

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

The cross product is

a × b =\begin{gathered}\left[\begin{array}{ccc}i&j&k\\-1&-3&-8\\7&4&-5\end{array}\right]\end{gathered}⎣⎢⎡i−17j−34k−8−5⎦⎥⎤

        = 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 .

Step-by-step explanation:

47, -61, 71>; yes