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If vec(a)= hat(i) - 2hat(j) + 5hat(k) an...

If `vec(a)= hat(i) - 2hat(j) + 5hat(k) and vec(b) = 2hat(i) + hat(j) -3hat(k)`, then `(vec(b) - vec(a)).(3 vec(a) +vec(b))` equal to?

Text Solution

Verified by Experts

The correct Answer is:
6
`vec(a).vec(b)` are any two vectors and `|vec(a)+ vec(b)| ge |vec(a)| + |vec(b)|`. It is possible only when `|vec(a)+vec(b)|= |vec(a)|+ |vec(b)|`, i.e `theta= 0^(@)`
According to parallel condition of two vectors i.e.,
`(c_(1))/(c_(2))= (a_(1))/(a_(2))`
`rArr (lamda)/(3)= (1)/(2) rArr lamda= (3)/(2) rArr 4 lamda= 6`
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