The cartesian equation of the plane passing through the point $(3, - 2, - 1)$ and parallel to the vectors $\to b =^i - 2^j + 4^k$ and $\to c = 3^i + 2^j - 5^k,$ is

2 x - 17 y - 8 z + 63 = 0

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3 x + 17 y + 8 z - 36 = 0

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2 x + 17 y + 8 z + 36 = 0

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3 x - 16 y + 8 z - 63 = 0

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Solution

The correct option is C $2 x + 17 y + 8 z + 36 = 0$
Required equation of plane is :
$∣ ∣ ∣ ∣ \begin{matrix} x - x_{1} & y - y_{1} & z - z_{1} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} x - 3 & y + 2 & z + 1 1 & - 2 & 4 3 & 2 & - 5 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow 2 x + 17 y + 8 z + 36 = 0$

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Similar questions

(5, - 1, 3)

^i + 2^j + 3^k

3^i -^j + 4^k

(5, 2, - 4)

3^i + 2^j - 8^k

2^i +^j +^k,^i + 2^j + 3^k

^i + 2^j +^k

(1, 2, 4)

\to r =^i + 2^j - 4^k + λ (2^i + 3^j + 6^k)

\to r =^i - 3^j + 5^k + μ (^i +^j -^k)

(9, 8, 10)

\frac{a}{\sqrt{b}} .

a + b

^i + 2^j + 3^j

\to r . (3^i + 4^j + 5^j)

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