If a line with direction ratios 2-2-1 intersects the line x-7-3-y-5-2-z-3-1 and x-1-2-y-1-4-z-1-3 at A and B then AB -A- 2 B- -2C- -3D- 3

The correct option is D 3A(7+3 α, 5 + 2α, 3 + α),B(2 β, 1 + 4 β, 1 + 3 β) Dr’s of AB are ( 2 ,2,1) 7+3 α 2 β/2 = 3 + α 2 β/1 = 4 + α 3 β/1 α = 2, β ...

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Byju's Answer

Standard XII

Mathematics

Angle between Two Line Segments

If a line wit...

Question

If a line with direction ratios $(2, 2, 1)$ intersects the line $\frac{x - 7}{3} = \frac{y - 5}{2} = \frac{z + 3}{1}$ and $\frac{x - 1}{2} = \frac{y + 1}{4} = \frac{z + 1}{3}$ at A and B then AB=.

\sqrt{2}

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2

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\sqrt{3}

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3

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Solution

The correct option is D $3$
$A (7 + 3 α, 5 + 2 α, 3 + α), B (2 β, - 1 + 4 β, - 1 + 3 β)$
Dr’s of AB are $(2, 2, 1)$
$\frac{7 + 3 α - 2 β}{2} = \frac{3 + α - 2 β}{1} = \frac{4 + α - 3 β}{1}$
$α = - 2, β = 1$ A(1,1,1) B(3,3,2) AB = 3

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Similar questions

Q. If a line with direction ratios

2 : 2 : 1

intersects the lines

\frac{x - 7}{3} = \frac{y - 5}{2} = \frac{z - 3}{1}

and

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

A

and

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Q. If a line with direction ratio

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and

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

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and

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and

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If a line with direction ratios(2,2,1) intersects the line x−73=y−52=z+31 and x−12=y+14=z+13 at A and B then AB=.

The correct option is D 3A(7+3α,5+2α,3+α),B(2β,−1+4β,−1+3β) Dr’s of AB are (2,2,1) 7+3α−2β2=3+α−2β1=4+α−3β1 α=−2,β=1 A(1,1,1) B(3,3,2) AB = 3

If a line with direction ratios $(2, 2, 1)$ intersects the line $\frac{x - 7}{3} = \frac{y - 5}{2} = \frac{z + 3}{1}$ and $\frac{x - 1}{2} = \frac{y + 1}{4} = \frac{z + 1}{3}$ at A and B then AB=.

The correct option is D $3$
$A (7 + 3 α, 5 + 2 α, 3 + α), B (2 β, - 1 + 4 β, - 1 + 3 β)$
Dr’s of AB are $(2, 2, 1)$
$\frac{7 + 3 α - 2 β}{2} = \frac{3 + α - 2 β}{1} = \frac{4 + α - 3 β}{1}$
$α = - 2, β = 1$ A(1,1,1) B(3,3,2) AB = 3