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Equation of a Plane : Vector Form

Find the vect...

Question

Find the vector equation of the line joining points $2^i +^j + 3^k$ and $- 4^i + 3^j -^k$ .

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Solution

Consider the given points be $A$ and $B$

$\begin{matrix} - - \to O A = 2^i +^j + 3^k - - \to O B = - 4^i + 3^j -^k \end{matrix}$

Therefore, coordinates of point $A$ and $B$ are $(2, 1, 3)$ and $(- 4, 3, - 1)$ respectively.

Direction ratios of the line $A B$ are proportional to $(- 4 - 2), (3 - 1), (- 1 - 3)$
i.e.
$3, - 1, 2$

Thus vector equation of the line is

$\to r = \to a + λ \to b$

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

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