Question

Answer with detailed steps
Q.):- Find the scalar and vector product of two vectors $\overrightarrow{A}=3\hat{i}-4\hat{j}+5\hat{k}$ and $\overrightarrow{B}=-2\hat{i}-\hat{j}+3\hat{k}$.

Answer 1

Scalar product, $C=\overrightarrow{A}.\overrightarrow{B}=(3\hat{i}-4\hat{j}+5\hat{k}).(-2\hat{i}-\hat{j}+3\hat{k})=\left(2\right)\left(3\right)+(-4)(-1)+\left(5\right)\left(3\right)=6+4+15=25$

Let the resultant vector product be $\overrightarrow{Q}$

$\therefore \overrightarrow{Q}=\overrightarrow{A}\times \overrightarrow{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& -4& 5\\ -2& -1& 3\end{array}\right|$

$\overrightarrow{Q}=(-12-(-5))\hat{i}-(9-(-10))\hat{j}+(-3-8)\hat{k}$

$\overrightarrow{Q}=-9\hat{i}-19\hat{j}-11\hat{k}$