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Equation of a Plane : Vector Form

Vector equati...

Question

Vector equation of the line $6 x - 2 = 3 y + 1 = 2 z - 2$ is

A

\to r =^i +^j + 3^k + λ (^i - 2^j + 3^k)

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B

\to r =^i - 2^j + 3^k + λ (\frac{1}{3}^i + \frac{1}{3}^j +^k)

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C

\to r = \frac{1}{3}^i - \frac{1}{3}^j +^k + λ (^i + 2^j + 3^k)

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D

\to r = - 2^i +^j - 2^k + λ (6^i + 3^j + 2^k)

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Solution

The correct option is B $\to r = \frac{1}{3}^i - \frac{1}{3}^j +^k + λ (^i + 2^j + 3^k)$
$6 x - 2 = 3 y + 1 = 2 z - 2$

$\frac{x - \frac{1}{3}}{\frac{1}{6}} = \frac{y + \frac{1}{3}}{\frac{1}{3}} = \frac{z - 1}{\frac{1}{2}}$

$\to r = \to a + λ \to b$

$a = (\frac{1}{3}, - \frac{1}{3}, 1), b = (\frac{1}{6}, \frac{1}{3}, \frac{1}{2})$

$v e l u e e q^{n} i s = (1, 2, 3)$

$\to r = \frac{1}{3} ˆ i - \frac{1}{3} ˆ j + ˆ k + λ (\frac{1}{6} ˆ i + \frac{1}{3} ˆ j + \frac{1}{2} ˆ k)$

$\to r = \frac{1}{3} ˆ i - \frac{1}{3} ˆ j + ˆ k + λ (ˆ i + 2 ˆ j + 3 ˆ k)$

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