Question

Find the angle between the vector having direction ratios $(3,4,5)$ and $(4,-3,5)$.

Answer 1

Vectors $3\hat{i}+4\hat{j}+5\hat{k}=\overrightarrow{a}$

$4\hat{i}-3\hat{j}+5\hat{k}=\overrightarrow{b}$

$cos\theta =\frac{\overrightarrow{a}\overrightarrow{b}}{\left|\overrightarrow{a}\overrightarrow{}b\right|}$

$cos\theta =\frac{(3\hat{i}+4\hat{j}+5\hat{k}),(4\hat{i}-3\hat{j}+5\hat{k})}{\sqrt{9+16+25}\sqrt{9+16+25}}$

$cos\theta =\left(\frac{25}{50}\right)$

$\left[\right(\theta =\frac{\pi }{3}{)}^c]$

$cos\theta =\frac{\overrightarrow{a}\overrightarrow{b}}{\left|\overrightarrow{a}\overrightarrow{}b\right|}$