Statement 1: Vector ` vec c=-5 hat i+7 hat j+2 hat k` is along the bisector of angel between ` vec a= hat i+2 hat j+2 hat ka n d vec b=8 hat i+ hat j-4 hat kdot` Statement 2: ` vec c` is equally inclined to ` vec a a n d vec b dot`

Options

A. Both the statements are true and statement 2 is the correct explanation for statement 1.
B. Both statements are true but statement 2 is not the correct explanation for statement 1.
C. Statement 1 is true and Statement 2 is false
D. Statement 1 is false and Statement 2 is true.

Answer

b

Explanation

A vector along the bisector is
` veca/(|veca|)+vecb/|vecb|= (-5hati+7hatj+2hatk)/9`
Hence `vecc = -5hati + 7hatj +2hatk` is along the bisectior. It is obvious that `vecc` makes an equal with `veca and vecb` However, statement 2 does not explain statment 1, as a vector equally inclined to given two vectors is not necessarily coplanar.