If and then find the projection of on

Find λ if the vectors and are coplanar.

If a line makes angles 90^{o}, 60^{o} and θ with x, y and z-axis respectively, where θ is acute, then find θ.

Write the element a_{23} of a 3 × 3 matrix A = (a_{jj}) whose elements a_{ij} are given by

Find the differential equation representing the family of curves where A and B are arbitrary constants.

Find the integrating factor of the differential equation

If find A^{2} – 5A + 4I and hence find a matrix X such that A^{2} – 5A + 4I + X = O.

OR

If find (A’)^{-1}.

If using properties of determinants find the value of f(2x) – f(x).

Find :

Integrate the following w.r.t. x

Evaluate :