If the direction cosines of two lines are 2 3 ,   2 3 ,   1 3 and 5 13 ,   12 13 ,   0 , then identify the direction ratios of a line which is bisecting one of the angle between them.

Question

If the direction cosines of two lines are 2 3 , &#160; 2 3 , &#160; 1 3 and 5 13 , &#160; 12 13 , &#160; 0 , then identify the direction ratios of a line which is bisecting one of the angle between them.

Aicharya · Accepted Answer

Given, the direction cosines of two lines are $(\frac{2}{3}, \frac{2}{3}, \frac{1}{3})$ and $(\frac{5}{13}, \frac{12}{13}, 0) .$

We know that, the direction ratios of the line bisecting the angle between the lines whose direction cosines are $(l_{1}, m_{1}, n_{1})$ and $(l_{2}, m_{2}, n_{2})$ are proportional to $⟨ l_{1} + l_{2}, m_{1} + m_{2}, n_{1} + n_{2} ⟩ .$

Hence, the required direction ratios are proportional to $⟨ \frac{2}{3} + \frac{5}{13}, \frac{2}{3} + \frac{12}{13}, \frac{1}{3} + 0 ⟩ = ⟨ \frac{41}{39}, \frac{62}{39}, \frac{13}{39} ⟩ .$

Thus, the direction ratios are $⟨ 41, 62, 13 ⟩ .$

If the direction cosines of two lines are 2 3 ,   2 3 ,   1 3 and 5 13 ,   12 13 ,   0 ,…

Solution

If the direction cosines of two lines are 2 3 , &#160; 2 3 , &#160; 1 3 and 5 13 , &#160; 12 13 , &#160; 0 ,…

Solution

If the direction cosines of two lines are 2 3 , 2 3 , 1 3 and 5 13 , 12 13 , 0 ,…