The direction cosines of two lines are langle | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the direction cosines of the two lines be $(l_1, m_1, n_1) = (\frac{\sqrt{3}}{2}, \frac{1}{4}, \frac{\sqrt{3}}{4})$ and $(l_2, m_2, n_2) = (-\

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(B) Let the direction cosines of the two lines be $(l_1, m_1, n_1) = (\frac{\sqrt{3}}{2}, \frac{1}{4}, \frac{\sqrt{3}}{4})$ and $(l_2, m_2, n_2) = (-\frac{\sqrt{3}}{2}, \frac{1}{4}, \frac{\sqrt{3}}{4})$.The cosine of the angle $	heta$ between the two lines is given by the formula $\cos 	heta = |l_1 l_2 + m_1 m_2 + n_1 n_2|$.Substituting the values:$\cos 	heta = |(\frac{\sqrt{3}}{2})(-\frac{\sqrt{3}}{2}) + (\frac{1}{4})(\frac{1}{4}) + (\frac{\sqrt{3}}{4})(\frac{\sqrt{3}}{4})|$$\cos 	heta = |-\frac{3}{4} + \frac{1}{16} + \frac{3}{16}|$$\cos 	heta = |-\frac{12}{16} + \frac{4}{16}| = |-\frac{8}{16}| = |-\frac{1}{2}| = \frac{1}{2}$.Since $\cos 	heta = \frac{1}{2}$,we have $	heta = 60^{\circ}$.Thus,the angle between the lines is $60^{\circ}$.

The direction cosines of two lines are $\langle\frac{\sqrt{3}}{2}, \frac{1}{4}, \frac{\sqrt{3}}{4}\rangle$ and $\langle-\frac{\sqrt{3}}{2}, \frac{1}{4}, \frac{\sqrt{3}}{4}\rangle$. Then the angle between the lines is equal to (in $^{\circ}$)

Similar Questions

If $a, b, c$ are the direction ratios of a line $L$ and $\ell, m, n$ are its direction cosines,then $\frac{a^2}{b^2+c^2}=$

If $\alpha, \beta, \gamma$ are the angles that a line makes with the coordinate axes,then which of the following is true?

If the direction cosines of a line are $\left(\frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}}\right)$ and $c-a=4$,then $ca=$

If the direction cosines $l, m, n$ of two lines satisfy the relations $l+m+n=0$ and $lm=0$,then the angle between those two lines is

If the direction cosines of two lines satisfy the equations $2l+m-n=0$ and $l^2-2m^2+n^2=0$, and $\theta$ is the angle between the lines, then $\cos \theta=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module