Find the projection of the line segment joini | vedclass

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

Question

(C) Let the points be $A(-1, 2, 3)$ and $B(-1, 4, 0)$.The direction ratios of the line segment $AB$ are $(x_2 - x_1, y_2 - y_1, z_2 - z_1) = (-1 - (-1

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(C) Let the points be $A(-1, 2, 3)$ and $B(-1, 4, 0)$.The direction ratios of the line segment $AB$ are $(x_2 - x_1, y_2 - y_1, z_2 - z_1) = (-1 - (-1), 4 - 2, 0 - 3) = (0, 2, -3)$.The line makes angles $\alpha = 45^{\circ}, \beta = 60^{\circ}, \gamma = 60^{\circ}$ with the coordinate axes.The direction cosines of the line are $l = \cos(45^{\circ}) = \frac{1}{\sqrt{2}}$,$m = \cos(60^{\circ}) = \frac{1}{2}$,and $n = \cos(60^{\circ}) = \frac{1}{2}$.The projection of a line segment with direction ratios $(a, b, c)$ on a line with direction cosines $(l, m, n)$ is given by $|al + bm + cn|$.Substituting the values: Projection $= |(0)(\frac{1}{\sqrt{2}}) + (2)(\frac{1}{2}) + (-3)(\frac{1}{2})| = |0 + 1 - \frac{3}{2}| = |-\frac{1}{2}| = \frac{1}{2}$.

Find the projection of the line segment joining the points $A(-1, 2, 3)$ and $B(-1, 4, 0)$ on a line which makes angles of $45^{\circ}, 60^{\circ},$ and $60^{\circ}$ with the coordinate axes.

Similar Questions

Find a vector $\vec{r}$ of magnitude $3 \sqrt{2}$ units which makes an angle of $\frac{\pi}{4}$ and $\frac{\pi}{2}$ with $y$ and $z$-axes,respectively.

$A$ line makes angles $\alpha, \beta, \gamma$ with the coordinate axes. If $\alpha + \beta = 90^\circ$,then $\gamma = \dots \dots ^\circ$.

The direction cosines of a line which makes equal acute angles with the coordinate axes are

The direction cosines of the line passing through $P(2, 3, -1)$ and the origin are

If the direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is

Vedclass Test Series

Exam Paper Generator

Online Exam Module