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General Form of a Straight Line

The point of ...

Question

The point of intersection of the following lines is:
$l_{1} : r (t) = (i - 6 j + 2 k) + t (i + 2 j + k)$
$l_{2} : R (u) = (4 j + k) + u (2 i + j + 2 k)$

at the tip of

r (7)

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at the tip of

R (4)

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(8, 8, 9)

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at the tip of

R (2)

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Solution

The correct options are
A $(8, 8, 9)$
B at the tip of $r (7)$
C at the tip of $R (4)$
$L_{1} = r (t) = (i - 6 j + 2 k) + t (i + 2 j + k)$
$L_{2} = R (u) = (4 j + k) + u (2 i + j + 2 k)$
$\Rightarrow r (7) = 8^i + 8^j + 9^k$
$\Rightarrow R (4) = 8^i + 8^j + 9^k$
Both the line intersect at the tip of $r (7)$ or $r (4)$
$ξ$ Clearly point of intersection is $(8, 8, 9)$ .
Hence, the answer is: at the tip of $r (7)$ , at the tip of $R (4)$ , $(8, 8, 9) .$

Suggest Corrections

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