The sides of a parallelogram are `2hati+4hat-5hatk and hati+2hatj+3hatk`. The unit vector parallel to one of the diagonal is (A) `1/sqrt(69)(hati+2hatj-8hatk)` (B) `1/sqrt(69)(-hati+2hatj+8hatk)` (C) `1/sqrt(69)(-hati-2hatj-8hatk)` (D) `1/sqrt(69)(hati+2hatj+8hatk)`

The sides of a parallelogram are 2hati +4hatj -5hatk and hati + 2hatj +3hatk . The unit vector parallel to one of the diagonals is

The sides of a parallelogram are 2 hati + 4 hatj -5 hatk and hati + 2 hatj + 3 hatk , then the unit vector parallel to one of the diagonals is

The diagonals of a parallelogram are given by -3hati+2hatj-4hatk and -hati+2hatj+hatk . Calculate the area of parallelogram.

If the diagonals of a parallelogram are 3 hati + hatj -2hatk and hati - 3 hatj + 4 hatk, then the lengths of its sides are

The scalar product of 2hati-3hatj+5hatk and 8hati+hatj+4hatk .

The unit vector parallel to the resultant vector of 2hati+4hatj-5hatk and hati+2hatj+3hatk is

Two vectors vecalpha=3hati+4hatj and vecbeta5hati+2hatj-14hatk have the same initial point then their angulr bisector having magnitude 7/3 be (A) 7/(3sqrt(6))(2hati+hatj-hatk) (B) 7/(3sqrt(3))(\hati+hatj-hatk) (C) 7/(3sqrt(3))(hati-hatj+hatk) (D) 7/(3sqrt(3))(hati-hatj-hatk)

A unit vector which is equally inclined to the vector hati, (-2hati+hatj+2hatk)/3 and (-4hatj-3hatk)/5 (A) 1/sqrt(51)(-hati+5hatj-5hatk) (B) 1/sqrt(51)(hati+5hatj+5hatk) (C) 1/sqrt(51)(hati+5hatj-5hatk) (D) 1/sqrt(51)(hati+5hatj+5hatk)

Show that vectors 2hati-3hatj+4hatk and -4hati+6hatj-8hatk are parallel

Let veca=hati+2hatj +hatk, vec=hati-hatj+hatk and vecc=hati+hatj-hatk . A vector in the plane of veca and vecb whose projection on vecc is 1/sqrt(3) is (A) 4hati-hatj+4hatk (B) hati+hatj-3hatk (C) 2hati+hatj-2hatk (D) 4hati+hatj-4hatk