Find the equation of the line in vector and in cartesian form that passes through the point with position vector `2 hat i- hat j+4 hat k` and is in the direction ` hat i+2 hat j- hat k`.

Explanation

It is given that the line passes through the point with position vector,

`a =2 i^- j^+4 k^...(1)b= i^+2 j^− k^...(2)`


It is known that a line through a point with position vector
a and parallel to b is given by the equation, r = a+λb


`⇒ r=2^i− ^j+4 ^k+λ( ^i+2 ^j−^k)`

This is the required equation of the line in vector form.

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