The line through `hati+3hatj+2hatk` and perpendicular to the lines `vecr=(hati+2hatj-hatk)+lamda(2hati+hatj+hatk)` and `vecr=(2hati+6hatj+hatk)+mu(hati+2hatj+3hatk)` is

Options

A. `vecr=(hati+2hatj-hatk)+lamda(-hati+5hatj-3hatk)`
B. `vecr=hati+3hatj+2hatk+lamda(hati-5hatj+3hatk)`
C. `vecr=hati+3hatj+2hatk+lamda(hati+5hatj+3hatk)`
D. `vecr=hati+3hatj+2hatk+lamda(-hati-5hatj-3hatk)`

Answer

b

Explanation

The required line passes through the point `hati+3hatj+2hatk` and is perpendicular to the lines `vecr= (hati+2hatj-hatk)+ lamda(2hati+hatj+hatk) and vecr= (2hati+ 6hatj+hatk)+mu (hati+ 2hatj+3hatk)`, therefore, it is parallel to the vector
`vecb= (2hati+hatj+ hatk)xx (hati+2hatj+3hatk)=(hati-5hatj+3hatk)`
Hence, the equation of the required line is
`" "vecr= (hati+3hatj+2hatk)+lamda(hati-5hatj+3hatk)`