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)`.

The vector equation of the line passing through the point vec(i)-2vec(j) + vec(k) and perpendicular to the vectors 2vec(i)-3vec(j)-vec(k), vec(i) + 4vec(j)-2vec(k) is

A unit vector normal to the plane through the points vec(i), 2vec(j) and 3vec(k) is

The vector area of the triangle formed by the points vec(i) -vec(j) + vec(k), 2vec(i) + vec(j) -2vec(k) and 3vec(i) + vec(j) + 2vec(k) is

The vector area of the parallelogram whose diagonals are vec(i) + 2vec(j) + 3vec(k), -vec(i) - 2vec(j) + vec(k) is

Equation of the plane containing the lines vec(r )= vec(i) + 2vec(j) -vec(k) + lamda (vec(i) + 2vec(j)-vec(k)), vec(r )=vec(i) + 2vec(j) -vec(k)+ mu (vec(i) + vec(j) + 3vec(k)) is

The area of the triangle formed by thepoints whose position vectors are 3vec(i) + vec(j), 5vec(i) + 2vec(j) + vec(k) and vec(i) -2vec(j) + 3vec(k) is (in sq.u)

The vector area of the parallelogram whose adjacent sides vec(i) + vec(j) + vec(k) and 2vec(i)-vec(j) + 2vec(k) is

Find the unit vectors perpendicular to both the vectors 2vec(i)- 3vec(j) + 5vec(k) and -vec(i) + 4vec(j) + 2vec(k)

Find the angle between the vectors vec(i) + 2vec(j) + 3vec(k) and 3vec(i) - vec(j) + 2vec(k) .