The projection of a line $P Q$, where $P$ is $(0,-1,3)$ and $Q$ is $(4,5,6)$ on a line whose direction ratios are $1,2,3$ is

JEE MATHEMATICS MCQ: DCS AND DRS

1 Easy

1 of 1

Application +4 | -1

The projection of a line

P Q

, where

P

(0,-1,3)

and

Q

(4,5,6)

on a line whose direction ratios are

1,2,3

View answer and explanation

Correct option: C

\frac{25}{\sqrt{14}}

Option C (

\frac{25}{\sqrt{14}}

) is correct because it represents the projection of the line PQ onto the given direction ratios, calculated using the formula for projection.

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\frac{2-x}{3}=\frac{3 y-2}{4 \lambda+1}=4-z

\frac{x+3}{3 \mu}=\frac{1-2 y}{6}=\frac{5-z}{7},

4 \lambda+9 \mu

\frac{x}{2}=\frac{y}{2}=\frac{z}{1}

\frac{x+2}{-1}=\frac{y-4}{8}=\frac{z-5}{4}

4 {~m}

2 {~kg}

10 {~kg}

45^{\circ}

60^{\circ}

X

Y

Z

\mathrm{AB}

-2 / \sqrt{17}

3 / \sqrt{17},-2 / \sqrt{17}

\mathrm{AB}=\sqrt{17}

\mathrm{A}

(3,-6,10)

\mathrm{B}

A B

45^{\circ}

120^{\circ}

X

Y

A B

\theta

Z

\theta