Question

For the vector a = 4i-6j+10k and b =-6i+9j-15k, what is axb? where i,j,k are unit vectors.

• -24î-54j-150k
• 1î-1j+1k
• 0î+0j+0k
• 3î-2j+0k

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Answer 1

ANSWER:

$\vec A × \vec B= 0 \hat i +0 \hat j +0 \hat k$

Answer 2

Solution:-Doing cross product is not a big task,,it is as like Simple multiplication,,,u have to just remember the following concept

,i×i=0, j×j=0,k×k=0,i×j=k, j×k=i, k×i=j

j×i=-k,k×j=-i i×k=-j

Now,

a×b=4i(9j-15k)-6j(-6i-15k)+10k(-6i+9j)

=(4i×9j)-(4i×15k)+(6i×6j)+(6j×15k)-(10k×6i)+(10k×9j)

=36(i×j)-(60)(i×k)+(36)(i×j)+(90)(j×k)-(60)(k×i)+(90)(k×j)

=-36k -60(-j) +36(k)+90(i) -60(j) +90(-i)

=-36k+60j+36k+90i-60j-90i

=(-36+36)k +(60-60)j +(90-90)i

=0i+0j+0k