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Find the equation of the line in vector and in Cartesian form that passes through the point with position vector `2hati -hatj+4hatk`  and is in the direction `hati + 2hatj - hatk`. - CBSE (Science) Class 12 - Mathematics

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Question

Find the equation of the line in vector and in Cartesian form that passes through the point with position vector `2hati -hatj+4hatk`  and is in the direction `hati + 2hatj - hatk`.

Solution

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

It is known that a line through a point with position vector `veca` and parallel to `vecb` is given by the equation, `vecr = veca + lambdavecb`

`=> vecr = 2hati - hatj +4hatk + lambda(hati+2hatj-hatk)`

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

This is the required equation of the given line in Cartesian form.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 11: Three Dimensional Geometry
Q: 5 | Page no. 477
Solution Find the equation of the line in vector and in Cartesian form that passes through the point with position vector `2hati -hatj+4hatk`  and is in the direction `hati + 2hatj - hatk`. Concept: Equation of a Line in Space.
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