If the vectors `vec(PQ)=-3hati+4hatj+4hatk and vec(PR)=5hati-2hatj+4hatk` are the sides of a triangle PQR, then the length o the median through P is (A) `sqrt(14)` (B) `sqrt(15)` (C) `sqrt(17)` (D) `sqrt(18)`

If the vectors vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk are the sides of a triangle ABC, then the length of the median through A is (A) sqrt(33) (B) sqrt(45) (C) sqrt(18) (D) sqrt(720

The vector vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk are sides of a triangle ABC. The length of the median through A is (A) sqrt(18) (B) sqrt(72) (C) sqrt(33) (D) sqrt(288)

If vecF = 3hati + 4hatj+5hatk and vecS=6hati +2hatj+5hatk , the find the work done.

If vecF=3hati-4hatj+5hatk " and " vecS=6hati+2hatj+5hatk , the find the work done.

If the position vectors of P and Q are (hati+3hatj-7hatk) and (5hati-2hatj+4hatk) , then |PQ| is

veca=hati-hatj+hatk and vecb=2hati+4hati+3hatk are one of the sides and medians respectively of a triangle through the same vertex, then area of the triangle is (A) 1/2 sqrt(83) (B) sqrt(83) (C) 1/2 sqrt(85) (D) sqrt(86)

If vec(OP)=2hati+3hatj-hatk and vec(OQ)=3hati-4hatj+2hatk find the modulus and direction cosines of vec(PQ) .

If vec(OP)=2hati+3hatj-hatk and vec(OQ)=5hati+4hatj-3hatk . Find vec(PQ) and the direction cosines of vec(PQ) .

Show that vectors 3hati-2hatj+2hatk,hati-3hatj+4hatk and 2hati-hatj-2hatk form a right angled triangle

Find the angle between the vectors 4hati-2hatj+4hatk and 3hati-6hatj-2hatk.