Question

The angle between the lines
`vecr=(hati+hatj+hatk)+lamda(hati+hatj+2hatk)`
and `vecr=(hati+hatj+hatk)+mu{(-sqrt(3)-1)hati+(sqrt(3)-1)hatj+4hatk}` is
A. `(pi)/6`
B. `(pi)/4`
C. `(pi)/3`
D. `(2pi)/3`

Answer 1

Correct Answer - C
Given lines are parallel to the vectors
`vecb_(1)=hati+hatj+2hatk` and `vecb_(2)=(-sqrt(3)-1)hati+(sqrt(3)-1)hatj+4hatk`
Let `theta` the angel between the given lines. Then,
`cos theta=(vecb_(1).vecb_(2))/(|vecb_(1)||vecb_(2)|)`
`impliescos theta=(-sqrt(3)-1+sqrt(3)-1+8)/(sqrt(1+1+4)sqrt((-sqrt(3)-1)^(2)+(sqrt(3)-1)^(2)+16))=1/2`
`implies theta=(pi)/3`