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If |vec(a)|=2 and |vec(b)|=3 , then |vec...

If `|vec(a)|=2 and |vec(b)|=3 `, then `|vec(a)xxvec(b)|^(2)+|vec(a).vec(b)|^(2)` is equal to

A

72

B

64

C

48

D

36

Text Solution

Verified by Experts

The correct Answer is:
D
`vec(a)xxvec(b)=|vec(a)||vec(b)|sin theta hat(n)`
`:. |vec(a)xxvec(b)|=|vec(a)||vec(b)|sin theta = 6 sin theta`
`& |vec(a).vec(b)|=|vec(a)||vec(b)| cos theta=6 cos theta`
`|vec(a)xxvec(b)|^(2)+|vec(a).vec(b)|^(2)=(6sin theta)^(2)+(6 cos theta)^(2)`
`=36(sin ^(2)theta+cos^(2)theta)`
=36
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