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.

Let A,B,C be points with position vectors r_1=2hati-hatj+hatk,r_2=hati+2hatj+3hatk and r_3=3hati+hatj+2hatk relative to the origin O. Find the shortest distance between point B and plane OAC.

Let A, B, C be points with position vectors r_(1)=2hati-hatj+hatk, r_(2)=hati+2hatj+3hatk and r_(3)=3hati+hatj+2hatk relative to the origin 'O'. The shortest distance between point B and plane OAC is

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) .

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

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

The position vectors of A,B,C are 2hati+hatj-hatk,3hati-2hatj+hatk and hati+4hatj-3hatk respectively. Show that A, B and C are collinear.

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.