Question

If $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ denote the position vectors of points A and B respectively and C is a point on AB such that AC = 2 CB, then write the position vector of C.

If A is an invertible square matrix of order 3 and |A| = 5, then find the value of |adj A|.

If A = $\left(\begin{array}{l l }3 & 4 \\ 2 & 3\end{array}\right)$then find A + A’., where A’ is transpose of A.

Given A = $\left(\begin{array}{l l l }4 & 2 & 5 \\ 2 & 0 & 3 \\ -1 & 1 & 0\end{array}\right)$ , write the value of det. $(2A A^{-1}).$

Write the projection of the vector $\stackrel{\rightarrow}{a}\$ = $2\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ on the vector $\stackrel{\rightarrow}{b}\$ = $\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} +2\stackrel{\wedge}{k}$.

The value of the determinant of a matrix A of order 3 × 3 is 4. Find the value of |5A|.

Find the differential equation of the family of lines passing through the origin.