Question: The angle between lines whose direction ratio are 1, 1, 2 and $\sqrt{3}$ – 1, $\sqrt{3}$ – 1, 4 ...

Question

The angle between lines whose direction ratio are 1, 1, 2 and $\sqrt{3}$ – 1, $\sqrt{3}$ – 1, 4 is

Answer 1

Apply cos q = $\frac{a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2}}{\sqrt{a_{1}^{2} + b_{1}^{2} + c_{1}^{2}}\sqrt{a_{2}^{2} + b_{2}^{2} + c_{2}^{2}}}$

Here a₁, b₁, c₁

̃ 2, –1, 1

a₂ , b₂, c₂ ̃ 1, 1, 2

\ cos q = $\frac{2(1) + 1( - 1) + 1(2)}{\sqrt{6}\sqrt{6}} = \frac{3}{6}$

cos q = $\frac{1}{2} = \theta = \frac{\pi}{3}$

Question: The angle between lines whose direction ratio are 1, 1, 2 and \(\sqrt{3}\) – 1, \(\sqrt{3}\) – 1, 4 ...