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If vec(A)=hat(i)+2hat(j)+3 hat(k), vec(B...

If `vec(A)=hat(i)+2hat(j)+3 hat(k), vec(B)=-hat(i)+hat(j)+4hat(k)` and `vec(C)=3hat(i)-3hat(j)-12 hat(k)`, then find the angle between the vectors `(vec(A)+vec(B)+vec(C))` and `(vec(A)xxvec(B))` in degrees.

Text Solution

Verified by Experts

The correct Answer is:
90
`vecP=vecA+vecB+vecC=3hati-5hatk` and `vecQ=vecAxxvecB=|(hati,hatj,hatk),(1,2,3),(-1,1,4)|=5hati-7hatj+3hatk`
Angle between `vecP` & `vecQ` is given by `costheta=(vecP.vecQ)/(PQ)=(15-15)/(PQ)=0rArrtheta=90^(@)`
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