A vector `veca=that+t^2hatj` is rotated through a righat angle passing through the x-axis. What is the vector in its new position `(tgt0)?` (A) `t^2hati-thatj` (B) `sqrt(t)hati-1/sqrt(t)hatj` (C) `-t^2hati+thatj` (D) `(t^2hati-thatj)/(tsqrt(t^2+1)`

If the vectors hati-hatj, hatj+hatk and veca form a triangle then veca may be (A) -hati-hatk (B) hati-2hatj-hatk (C) 2hati+hatj+hatjk (D) hati+hatk

A vector hati+sqrt(3)hatj rotates about its tail through an angle 60^(@) in clockwise direction then the new vector is

The vector equation barr=hati-2hatj-hatk+t(6hatj-hatk) , represents a line passing through points

Given two vectors are hati-hatj and hati+2hatj . The unit vector coplanar with the two vectors nad perpendicular to first is (A) 1/sqrt(2)(hati+hatj) (B) 1/sqrt(5)(2hati+hatj) (C) +-1/sqrt(2)(hati+hatj) (D) none of these

The vector equation of a line passing through the point with position vector 2hati - hatj - 4hatk and is in the direction of hati - 2hatj + hatk is

Find the vector equation of the plane passing through the point hati + hatj -2hatk and hati + 2hatj + hatk, 2hati - hatj + hatk.

The vector equation of a line passing through the point hati + 2hatj + 3hatk and perpendicular to the vectors hati +hatj + hatk and 2hati - hatj + hatk is

A unit vector perpendicular to the plane passing through the points whose position vectors are hati-hatj+2hatk, 2hati-hatk and 2hati+hatk is

The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk and is coplanar with the vectors 2hati+hatj+hatk and hati-hatj+hatk is (A) (2hati-6hatj+hatk)/sqrt(41) (B) (2hati-3hatj)/sqrt(3) (C) 3hatj-hatk)/sqrt(10) (D) (4hati+3hatj-3hatk)/sqrt(34)