List of top Mathematics Questions on Direction Cosines and Direction Ratios of a Line asked in MHT CET

The direction cosines \(l,m,n\) of the two lines are connected by the relations \(l+m+n=0\) and \(lm=0\), then the angle between the lines is....

The position vector of a point \(P\), such that \(OP\) inclined to the X axis at \(45^{\circ }\) and to the Y axis at \(60^{\circ }\) and \(|OP|=12\) units is:

If the direction cosines of the line \(\frac{2x+5}{3}=\frac{2-3z}{-1};3y=-2\) are \(\frac{9}{\sqrt{85}},m,\frac{2}{\sqrt{85}}\) then the value of \(m\) is:

If the line \(\frac{x+4}{a}=\frac{y-2}{b}=\frac{z+1}{c}\) passes through the point \((-3,1,-2)\) and its direction is chosen such that it makes an acute angle \(\gamma\) with the positive direction of Z- axis, then value of \(\cos \gamma\) is:

If \(l,m,n\) are direction cosines of a vector \(\bar{r}\) such that \(l+m+n=1\) and \(l^{2}+m^{2}+n^{2}=1\), then:
(where \(l,m,n\geq 0\))

If the points \(A(1,p,1),B(2,5,-1),C(q,11,r)\) are collinear. If the line passing through these points is perpendicular to the vector \(4\hat{i}-2\hat{j}+\hat{k}\), then the value of \(p+q+r\) is

A line makes the same angle \(\alpha\) with each of the \(X\) and \(Z\) axes. If the angle \(\beta\) which it makes with the \(Y\)-axis is such that \(\sin ^{2}\beta =2\sin ^{2}\alpha\), then the value of \(\cos ^{2}\alpha\) is ...

If \(α,β,γ\) are the direction angles of the line \(x = 4z+3\) and \(y = 2-3z\), then the value of \(cosα+cosβ+cosγ\) is...

The angle between a diagonal and one of its edges of a cube is ...................

The direction cosines of a line which is perpendicular to the lines \(\frac{x-7}{2} = \frac{y+17}{-3} = \frac{z-6}{1}\) and \(\frac{x+5}{1} = \frac{y+3}{2} = \frac{z-6}{-2}\) are...

If a unit vector makes angles \(\frac{π}{4}\) with \(\hat{i}\), \(\frac{π}{3}\) with \(\hat{j}\) and \(θ\in (0,π)\) with \(\hat{k}\), then a value of \(θ\) is equal to...

The vector \(\overset{̄}{r}\) whose magnitude is \(3\sqrt{2}\) units and which makes angles of \(\frac{π}{4}\) and \(\frac{π}{2}\) with the positive y- and z-axes respectively is....

If a line makes angles \(α,β,γ\) with the coordinate axes, then the sum of values of \(sin^2α+sin^2β+sin^2γ\) and \(cos2α+cos2β+cos2γ\) is ...

A vector \(\overset{̄}{r}\) of magnitude \(3\sqrt{2}\) units which makes angles of \(\frac{π}{4}\) and \(\frac{π}{2}\) respectively with Y and Z axes is

The angle between lines whose direction cosines satisfy the equation $l + m + n = 0$ and $l^2 - m^2 - n^2 = 0$, is ______.

The angle between the lines whose direction cosines are \[ \frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2} \quad \text{and} \quad \frac{-\sqrt{3}}{4}, \frac{1}{2}, \frac{1}{\sqrt{3}} \] is

The angle between the lines whose direction cosines satisfy the equations: \[ l + m + n = 0 \quad \text{and} \quad m^2 + n^2 - l^2 = 0 \] Find the angle between the two lines.

The coordinates of the point $P \equiv (1,2,3)$ and $O \equiv (0,0,0)$ are given. The direction cosines of $\overline{OP}$ are

The direction cosines $\ell, m, n$ of the line $\frac{x+2}{2}=\frac{2y-5}{3} ; z=-1$ are

The angle between a line with direction ratios 2, 2, 1 and a line joining $(3, 1, 4)$ and $(7, 2, 12)$ is