Find the vector equation of the plane passing through the points.
`vec(i)-2vec(j)+5vec(k), -5vec(j)-vec(k)` and `-3vec(j)+5 vec(j)`.

Find the angle between the vectors : vec(a)=3vec(i)-2vec(j)+vec(k) and vec(b)=vec(i)-2vec(j)-3vec(k)

The Cartesian equation of the plane passing through the point (3,-2,-1) and parallel to the vectors vec b=i-2j+4k and vec c=3i+2j-5k

| 2vec i-3vec j + vec k | =

If the projection of vec(i)+3vec(j)+7vec(k) on 2vec(i)-3vec(j)+6vec(k) is ___________.

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

The cartesian equation of the plane perpendicular to vector 3vec i-2vec j-2vec k and passing through the point 2vec i+3vec j-vec k i

Find the unit vector in the direction of the vector vec a + vec b if vec a =vec i +2 vec j + 3 vec k and vec b = 2 vec i + 3 vec j + 5 vec k .

The value of 'a',for which the points A,B,C with position vectors 2vec i-vec j+vec k+vec k,vec i-3vec j-5vec k, and avec i-3vec j+vec k are vertices of a right angled triangle with /_C=(pi)/(2) are

If the vectors 2vec(i)-qvec(j)+3vec(k) and 4vec(i)-5vec(j)+6vec(k) are collinear, the value of q is

Find a unit vector which is perpendicular to each of the vectors 3vec i+2vec j-vec k and 12vec i+5vec j-5vec k