बिंदुओं P(2hati+3hatj+3hatk) और Q(4hati+hatj-... को मिलाने वाले रेखाखंड का मध्य बिंदु ज्ञात कीजिए।

Prove that: (2hati+3hatj)xx(hati+2hatj)=hatk

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

Find the area of the triangle formed by the tips of the vectors vec(a) = hati - hatj - 3hatk, vec(b) = 4hati - 3hatj +hatk and vec(c) = 3 hati - hatj +2 hatk .

Find the shortest distance between the lines bar(r) = (4hati - hatj) + lamda(hati + 2hatj - 3hatk) and bar(r) = (hati - hatj + 2hatk) + mu(hati + 4hatj - 5hatk).

The vectors P = 2hati+b hatj+2hatk and Q=hati+hatj+hatk will be perpendicular if -

Find a unit vector in the diection of the vector. (i) (3hati + 4hatj - 5hatk) , (ii) (3hati - 2hatj + 6hatk) (iii) (hati + hatk) , (iv) (2hati + hatj + 2hatk)

If p=7hati-2hatj+3hatk and q=3hati+hatj+5hatk , then find the the magnitude of p-2q.