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# Find the Vector Equation of the Line Passing Through (1, 2, 3) and Parallel to the Planes Vecr = (Hati - Hatj + 2hatk) = 5And Vecr.(3hati + Hatj + Hatk) = 6 - CBSE (Commerce) Class 12 - Mathematics

ConceptPlane Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point

#### Question

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr = (hati - hatj + 2hatk)  = 5and vecr.(3hati + hatj + hatk) = 6

#### Solution

Let the required line be parallel to vector vecb given by,

vecb = b_1hati + b_2hatj + b_3hatk

The position vector of the point (1, 2, 3) is veca = hati + 2hatj + 3hatk

The equation of line passing through (1, 2, 3) and parallel to vecbis given by, This is the equation of the required line.

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#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 11: Three Dimensional Geometry
Q: 19 | Page no. 499

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Solution Find the Vector Equation of the Line Passing Through (1, 2, 3) and Parallel to the Planes Vecr = (Hati - Hatj + 2hatk) = 5And Vecr.(3hati + Hatj + Hatk) = 6 Concept: Plane - Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point.
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