# 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. - Mathematics

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 Class 12 Maths
Chapter 11 Three Dimensional Geometry
Q 5 | Page 477