Equation of the line which passes through the point with p.v. (2, 1, 0) and perpendicular to the plane containing the vectors $ˆ i + ˆ j a n d ˆ j + ˆ k$ is

\to r = (2, 1, 0) + t (1, - 1, 1)

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\to r = (2, 1, 0) + t (- 1, 1, 1)

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\to r = (2, 1, 0) + t (1, 1, - 1)

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\to r = (2, 1, 0) + t (1, 1, 1)

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Solution

The correct option is A $\to r = (2, 1, 0) + t (1, - 1, 1)$
if line perpendicular to plane then eq
$\to r = p o s i t i o n v e c t o r \to a + t (n o r m a l v e c t o r \to n)$
normal vector of plane
Given $\to a =^i +^j$
$\to b =^j +^k$
$\to n = \to a \times \to b$
$\to a \times \to b = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & 1 & 0 0 & 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$\to a \times \to b =^i (1 - 0) -^j (1 - 0) +^k (1 - 0)$
$\to a \times \to b =^i -^j +^k$
eq become
$\to r = (2, 1, 0) + t (1, - 1, 1)$

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