The correct option is B −5^i+^j+5^k
Let the required vector be →a=x^i+y^j+z^k. It makes equal angles with the vectors.
→b=13(^i−2^j−2^k),→c=15(−4^i−3^k),→d=^j
∴→a.→b=→a.→c=→a.→d [∵→b,→c,→d are unit vectors]
∴13(x−2y+2z)=15(−4x−3z)=y
⇒x−2y+2=3y and −4x−5y−3z=0
⇒x−5y+2z=0 and 4x+5y+3z=0
Solving these equations, we get x= -z and x =-5y.
∴x−5=y1=z5orx5=y−1=z−5
⇒→a=−5^i+^j+5^k or →a=5^i−^j−5^k