If the angle between the lines whose directio | vedclass

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

Question

(B) Given the direction cosines of two lines as $(l_1, m_1, n_1) = \left(-\frac{2}{\sqrt{21}}, \frac{C}{\sqrt{21}}, \frac{1}{\sqrt{21}}\right)$ and $(

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) Given the direction cosines of two lines as $(l_1, m_1, n_1) = \left(-\frac{2}{\sqrt{21}}, \frac{C}{\sqrt{21}}, \frac{1}{\sqrt{21}}\right)$ and $(l_2, m_2, n_2) = \left(\frac{3}{\sqrt{54}}, \frac{3}{\sqrt{54}}, -\frac{6}{\sqrt{54}}\right)$.Since the angle between the lines is $\frac{\pi}{2}$,the lines are perpendicular.For perpendicular lines,the condition is $l_1 l_2 + m_1 m_2 + n_1 n_2 = 0$.Substituting the values:$\left(-\frac{2}{\sqrt{21}}\right) \left(\frac{3}{\sqrt{54}}\right) + \left(\frac{C}{\sqrt{21}}\right) \left(\frac{3}{\sqrt{54}}\right) + \left(\frac{1}{\sqrt{21}}\right) \left(-\frac{6}{\sqrt{54}}\right) = 0$$\frac{-6}{\sqrt{21}\sqrt{54}} + \frac{3C}{\sqrt{21}\sqrt{54}} - \frac{6}{\sqrt{21}\sqrt{54}} = 0$Multiplying by $\sqrt{21}\sqrt{54}$ on both sides:$-6 + 3C - 6 = 0$$3C - 12 = 0$$3C = 12$$C = 4$.

If the angle between the lines whose direction cosines are $\left(-\frac{2}{\sqrt{21}}, \frac{C}{\sqrt{21}}, \frac{1}{\sqrt{21}}\right)$ and $\left(\frac{3}{\sqrt{54}}, \frac{3}{\sqrt{54}}, -\frac{6}{\sqrt{54}}\right)$ is $\frac{\pi}{2}$,then the value of $C$ is

Similar Questions

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$,then the angle between them is

The angle between the lines with direction ratios $\left( \frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2} \right)$ and $\left( \frac{\sqrt{3}}{4}, \frac{1}{4}, -\frac{\sqrt{3}}{2} \right)$ is ......... $^o$.

$A$ straight line is equally inclined to all the three coordinate axes. Then,the angle made by the line with the $y$-axis is

Let the direction cosines of two lines satisfy the equations: $4l+m-n=0$ and $2mn+10nl+3lm=0$. Then the cosine of the acute angle between these lines is:

Find the angle between two lines whose direction cosines are given by the relations $l + m + n = 0$ and $l^2 + m^2 - n^2 = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module