निम्न समतलके सदिश समीकरणको करतीय समीकरण में बदलिएvec(r ).(2hati+3hatj-4hatk)/sqrt(29)=1 | 12 | ...

Angle between the planes: (i) vec(r). (hati - 2 hatj - hatk) = 1 and vec(r). (3 hati - 6 hatj + 2 hatk) = 0 (ii) vec(r). (2 hati + 2 hatj - 3 hatk ) = 5 and vec(r) . ( 3 hati - 3 hatj + 5 hatk ) = 3

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

Show that the vectors 2hati -3hatj+4hatk and -4hati+6hatj-8hatk are collinear.

The angle between the two vectors -2hati+3hatj+hatk and hati+2hatj-4hatk is -

The angle between the two vectors -2hati+3hatj-hatk and hati+2hatj+4hatk is

Find the shortest distance between the lines: (i) vec(r) = 6 hat(i) + 2 hat(j) + 2 hatk + lambda (hati - 2hatj + 2 hatk) and vec(r) = - 4 hati - hatk + mu (3 hati - 2 hatj - 2 hatk ) (ii) vec(r) = (4 hat(i) - hat(j)) + lambda (hati + 2hatj - 3 hatk) and vec(r) = (hati - hatj + 2hatk) + mu (2 hati + 4 hatj - 5 hatk ) (iii) vec(r) = (hati + 2 hatj - 4 hatk) + lambda (2 hati + 3 hatj + 6 hatk ) and vec(r) = (3 hati + 3 hatj + 5 hatk) + mu (-2 hati + 3 hatj + 6 hatk )

(i) Find the distance of the point (-1,-5,-10) from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk) and the plane vec(r).(hati - hatj + hatk) = 5. (ii) Find the distance of the point with position vector - hati - 5 hatj - 10 hatk from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - hatj + hatk)= 5. (iii) Find the distance of the point (2,12, 5) from the point of intersection of the line . vec(r) = 2 hati - 4 hatj + 2 hatk + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - 2 hatj + hatk ) = 0.

A body moves from a position vec(r_(1))=(2hati-3hatj-4hatk) m to a position vec(r_(2))=(3hati-4hatj+5hatk)m under the influence of a constant force vecF=(4hati+hatj+6hatk)N . The work done by the force is :

Show that the vectors 2hati-3hatj+4hatk and -4hati+6hatj-8hatk are collinear.