Consider points A,B,C annd D with position vectors `7hati-4hatj+7hatk,hati-6hatj+10hatk,-1hati-3hatj+4hatk and 5hati-hatj+5hatk`, respectively. Then, ABCD is

Consider points A, B, C and D with position vectors 7 hati - 4 hat j + 7 hat k , hati - 6 hat j + 10 hat k , - hati - 3 hatj + 4 hatk and 5 hati - hatj + 5 hatk respectively. Then, ABCD is a

Show that the four points A,B,C and D with position vectors 4hati+5hatj+hatk, -hatj-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk) respectively, are coplanar.

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

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 the point A, B, C and D are 3hati-2hatj -hatk, 2hati+3hatj-4hatk, -hati+hatj+2hatk and 4hati+5hatj +lamda hatk , respectively. If the points A, B, C and D lie on a plane, find the value of lamda .

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

If three points A, B and C have position vectors hati + x hatj + 3 hatk, 3 hati + 4 hatj + 7 hatk and y hati -2hatj - 5 hatk respectively are collinear, then (x, y) =

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

The volume of the tetrahedron whose vertices are the points with positon vectors hati-6hatj+10hatk, -hati-3hatj+7hatk, 5hati-hatj+lambdahatk and 7hati-4hatj+7hatk is 11 cubic units if the value of lamda is