If unit vectors `hati and hatj` are at right angles to each other and `p=3hati+4hatj,q=5hati,4r=p+q and 2s=p-q`, then

Find a unit vector vecc if -hati+hatj-hatk bisects the angle between vectors vecc and 3hati+4hatj .

Find a unit vector vecc if -hati+hatj-hatk bisects the angle between vectors vecc and 3hati+4hatj .

If P(-1,2) and Q(3,-7) are two points, express the vector PQ in terms of unit vectors hati and hatj also, find distance between point P and Q . What is the unit vector in the direction of PQ ?

If the vectors vecA=2hati+4hatj and vecB=5hati-phatj are parallel to each other, the magnitude of vecB is

If the vector -hati +hatj-hatk bisects the angle between the vector vecc and the vector 3hati +4hatj, then the vector along vecc is

Prove that the following vectors are at righat angle: 2hati+5hatj+hatk, 3hati-2hatj+4hatk

Calculate the components of a vector of magnitude unity which is at right angles to the vectors 2hati+hatj-4hatk and 3hati+hatj-hatk .

The unit vector perpendicular to the vectors 6hati+2hatj+3hatk and 3hati-6hatj-2hatk , is

A unit vector in the xy-plane that makes an angle of pi/4 with the vector hati+hatj and an angle of 'pi/3' with the vector 3hati-4hatj is

Show that the points A,B and C having position vectors (3hati - 4hatj - 4hatk), (2hati - hatj + hatk) and (hati - 3hatj - 5hatk) respectively, from the vertices of a right-angled triangle.