A plane P passes through the line of intersection of the planes 2x minus y 3z 2 x y minus z 1and the...........

Mathematics (NDA) Coordinate Geometry

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A plane P passes through the line of intersection of the planes 2x − y + 3z = 2, x + y − z = 1and the point (1, 0, 1).

What are the direction ratios of the line of intersection of the given planes?

< 2, − 5, 3 >

< 1, − 5, − 3 >

< 2, 5, 3 >

< 1, 3, 5 >

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Explanation:

Given equations of plane are
2x − y + 3z = 2 ...(i)
and x + y − z = 1 ...(ii)
Let the direction ratios of line of intersection be < a, b, c >.
$\therefore$ 2a − b + 3c = 0 ...(iii)
and a + b − c = 0 [ $\because$ a₁a₂+b₁b₂+c₁c₂=0 ] ...(iv)
On solving Eqs (iii) and (iv), we get