Line L1 is parallel to vector α=−3i^+2j^+4k^ and passes through a point A(7,6,2) and line L2 is parallel vector β=2i^+j^+3k^ and point B(5,3,4)˙ Now a line L3 parallel to a vector r=2i^−2j^−k^ intersects the lines L1andL2 at points CandD, respectively, then find ∣∣CD∣∣˙

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Line {L}_{{1}} is parallel to vector {}=-{3}{{i}}+{2}{{j}}+{4}

Question

Line $L_{1}$ is parallel to vector $α = - 3 \hat{i} + 2 \hat{j} + 4 \hat{k}$ and passes through a point $A (7, 6, 2)$ and line $L_{2}$ is parallel vector $β = 2 \hat{i} + \hat{j} + 3 \hat{k}$ and point $B (5, 3, 4) ˙$ Now a line $L_{3}$ parallel to a vector $r = 2 \hat{i} - 2 \hat{j} - \hat{k}$ intersects the lines $L_{1} a n d L_{2}$ at points $C a n d D,$ respectively, then find $∣ ∣ C D ∣ ∣ ˙$

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Jack Discussed

Line

L_{1}

is parallel to vector

α = - 3 \hat{i} + 2 \hat{j} + 4 \hat{k}

and passes through a point

A (7, 6, 2)

and line

L_{2}

is parallel vector

β = 2 \hat{i} + \hat{j} + 3 \hat{k}

and point

B (5, 3, 4) ˙

Now a line

L_{3}

parallel to a vector

r = 2 \hat{i} - 2 \hat{j} - \hat{k}

intersects the lines

L_{1} a n d L_{2}

at points

C a n d D,

respectively, then find

∣ ∣ C D ∣ ∣ ˙

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