The angle between the lines whose direction cosines satisfy the e… - Vidyadip

MCQ

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$, ${l^2} + {m^2} - {n^2} = 0$ is given by

A
$\frac{{2\pi }}{3}$
B
$\frac{\pi }{6}$
C
$\frac{{5\pi }}{6}$
✓
$\frac{\pi }{3}$

✓

Answer

Correct option: D.

$\frac{\pi }{3}$

d
(d) $l + m + n = 0,\,\,{l^2} + {m^2} - {n^2} = 0$ and ${l^2} + {m^2} + {n^2} = 1$

Solving above equations, we get $m = \pm \frac{1}{{\sqrt 2 }},\,\,n = \pm \frac{1}{{\sqrt 2 }}$ and $l = 0$.

$\therefore \,\,\,\theta = \frac{\pi }{3}$ or $\frac{\pi }{2}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $m$ is the $A.M$ of two distinct real numbers $ l$ and $n (l,n>1) $ and $G_1, G_2$ and $G_3$ are three geometric means between $l$ and $n$ then $G_1^4 + 2G_2^4 + G_3^4$ equals :

If the vertices of a triangle have integral coordinates, then the triangle is

The sum to $20$ terms of the series $2.2^2-3^2+2.4^2-5^2+2.6^2-\ldots \ldots$ is equal to $........$.

If the vectors $2i + j - k,\, - i + 2j + \lambda k$ and $ - 5i + 2j - k$ are coplanar, then the value of $\lambda $ is equal

The diameter of the circle, whose centre lies on the line $x+y=2$ in the first quadrant and which touches both the lines $x=3$ and $y=2,$ is

The lines $y - y_1 = m (x - x_1) \pm a \,\sqrt {1\,\, + \,\,{m^2}} $ are tangents to the same circle . The radius of the circle is :

Three players play a total of $9$ games. In each game, one person wins and the other two lose; the winner gets $2$ points and the losers get $-1$ each. The number of ways in which they can play all the $9$ games and finish each with a zero score is

Let the circumcentre of a triangle with vertices $A ( a , 3), B ( b , 5)$ and $C ( a , b ), ab >0$ be $P (1,1)$. If the line $AP$ intersects the line $BC$ at the point $Q \left( k _{1}, k _{2}\right)$, then $k _{1}+ k _{2}$ is equal to.

Let $p(x)$ be a polynomial of degree $4$ having extremum at $x=1,2$ and $\lim _{x \rightarrow 0}\left(1+\frac{p(x)}{x^2}\right)=2 .$ Then the value of $p(2)$ is

Give the correct order of initials $T$ or $F$ for following statements. Use $T$ if statement is true and $F$ if it is false.
Statement $-1$ : If $A$ is an invertible $3 × 3$ matrix and $B$ is a $3 × 4$ matrix, then $A^{-1}B$ is defined
Statement $-2$ : It is never true that $A + B, A - B$, and $AB$ are all defined.
Statement $-3$ : Every matrix none of whose entries are zero is invertible.
Statement $-4$ : Every invertible matrix is square and has no two rows the same.