Find vector equation of line passing through point - - 2- - 3k- and perpendicular to vector - - - - k- and 2- - - - 3k-

Equation of line passing through i + 2j 3k Then, the equation is x 1/a = y 2/b = z 3/c Line is ∥ to vector : ( i + j + k) ×( 2i + j ...

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Standard XII

Mathematics

Equation of a Plane : Vector Form

Find vector e...

Question

Find vector equation of line passing through point $^i + 2^j + 3^k$ and perpendicular to vector $^i +^j +^k$ and $2^i +^j + 3^k$

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Solution

Equation of line passing through $ˆ i + 2 ˆ j - 3 ˆ k$
Then, the equation is $\frac{x - 1}{a} = \frac{y - 2}{b} = \frac{z - 3}{c}$
Line is $∥$ to vector : $(ˆ i + ˆ j + ˆ k) \times (2 ˆ i + ˆ j + 3 ˆ k)$
$= ∣ ∣ ∣ ∣ ∣ \begin{matrix} ˆ i & ˆ j & ˆ k 1 & 1 & 1 2 & 1 & 3 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$= ˆ i (3 - 1) - ˆ j (3 - 2) + ˆ k (1 - 2)$
$= 2 ˆ i - ˆ j - ˆ k$
Hence,
Equation of line : $\frac{x - 1}{2} = \frac{y - 2}{- 1} = \frac{z - 3}{- 1}$ .

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Find vector equation of line passing through point ^i+2^j+3^k and perpendicular to vector ^i+^j+^k and 2^i+^j+3^k

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Find vector equation of line passing through point $^i + 2^j + 3^k$ and perpendicular to vector $^i +^j +^k$ and $2^i +^j + 3^k$