Let A,B,C be points with position vectors `2hati-hatj+hatk,hati+2hatj+3hatkand 3hati+hatj+2hatk` respectively. Find the shortest distance between point B and plane OAC.

Let A,B,C be points with position vectors 2hati-hatj+hatk,hati+2hatj+hatkand 3hati+hatj+2hatk respectively. Find the shortest distance between point B and plane OAC.

Show that the points A, B and C with position vectors -2hati+3hatj+5hatk, hati+2hatj+3hatk and 7hati-hatk respectively are collinear

The point having position vectors 2hati+3hatj+4hatk,3hati+4hatj+2hatk and 4hati+2hatj+3hatk are the vertices of

If A, B, C and D are the points with position vectors hati-hatj+hatk,2hati-hatj+3hatk,2hati-3hatkand3hati-2hatj+hatk respectively, then find the projection of vec(AB)andvec(CD) .

The values of a for which the points A, B, and C with position vectors 2hati - hatj + hatk, hati - 3hatj - 5hatk, and ahati - 3hatj + hatk ,respectively, are the vertices of a right-angled triangle with C = pi/2 are

The points with position vectors alpha hati+hatj+hatk, hati-hatj-hatk, hati+2hatj-hatk, hati+hatj+betahatk are coplanar if

Show that the vectors hati-3hatj+2hatk,2hati-4hatj-hatk and 3hati+2hatj-hatk and linearly independent.

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.

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.

The position vectors of points A,B and C are hati+hatj,hati + 5hatj -hatk and 2hati + 3hatj + 5hatk , respectively the greatest angle of triangle ABC is