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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

#### 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.

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#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 11: Three Dimensional Geometry
Q: 5 | Page no. 477

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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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