Question

The two vectors $:{\hat{j}}+{\hat{k}}$ and $3\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ represent the two sides AB and AC, respectively of $\Delta A B C.$ Find the length of the median through A.

If A is a square matrix and | A | = 2, then write the value of | AA’ |, where A’ is the transpose of matrix A.

Write the value of $\textstyle\int\!{\frac{1-\sin x}{\cos^{2}x}}\,d x\,.$

If for any 2 × 2 square matrix A, A(adj A) = $\left(\begin{array}{l l }8 & 0 \\ 0 & 8\end{array}\right)$ , then write the value of |A|.

If A = $[a_{i j}]$ is is a matrix of order 2 × 2, such that |A| = –15, and $C_{i j}$ represents the cofactor of $a_{i j}$ , then find $a_{21}c_{21}+a_{22}c_{22}$

Find the projection of vector $\stackrel{\rightarrow}{a}\$ = $2\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} +2\stackrel{\wedge}{k}$ on the vector $\stackrel{\rightarrow}{b}\$ = $2\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$

Find the scalar components of the vector $\stackrel{\rightarrow}{A B}$ with initial point A(2,1) and terminal point B (– 5, 7).