If the position vectors of the points A and B respectively are i+2j-3k and j-k find the direction cosines of AB

If the position vectors of the points A and B are 3i+j+2k and i-2 j-4k respectively, then the equation of the plane through B and perpendicular to AB is

If the position vectors of A and B are 3i-2j+k and 2i+4j+3k then |vec AB| =

If the position vectors of A and B are 3i - 2i + k and 2i + 4j - 3k then the length of AB is

The position vector of a point C with respect to B is hat i +hat j and that of B with respect to A is hati-hatj . The position vector of C with respect to A is

The position vectors of two points P and Q are hat(i)+2hat(j)-hat(k)" and "-hat(i)+hat(j)+hat(k) respectively. Find the position vector of a point R which divides the line bar(PQ) in the ratio 2 : 1 internally.

Find the position vectors of a point R which divides the line joining two points P and Q whose position vectors are hat(i)+2hat(j)-hat(k)- and - hat(i)+hat(j)-hat(k) respectively, in the ration 2:1 . (i) Internally, (ii) Externally.

The values of 'a' for which the points A, B, C with position vectors 2i-j+k, i-3j-5k and ai-3j+k respectively are the vertices of a right angled triangle with C = pi/2 are

The position vector of a point laying on the line joining the points whose position vectors are i+j-k and i-j+k is

The three points whose position vectors are i+2j+3k, 3i+4j+7k, and -3i-2j-5k