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Equation of a Plane : Vector Form

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Question

Find the vector equation of the line which passes through the point with position vector $4^i -^j + 2^k$ and is in the direction of $- 2^i +^j +^k$ .

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Solution

Let $\to a = 4^i -^j + 2^k, \to b = - 2^i +^j +^k$

Equation of the line passing through point $\to a$ and having direction $\to b$ is $\to r = \to a + λ \to b$

Thus the vector equation of the line is $\to r = 4^i -^j + 2^k + λ (- 2^i +^j +^k)$

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