A straight line passes through (1, -2, 3) and perpendicular to the plane $2 x + 3 y - z = 7$ .Find the direction ratios of normal to plane.

< 2, 3, - 1 >

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< 2, 3, 1 >

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< - 1, 2, 3 >

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None of the above

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Solution

The correct option is A $< 2, 3, - 1 >$
$concept: for any plane a x + b y + c z + d = 0, normal vector to this plane is a^i + b^j + c^k$
the normal vector of the plane $2 x + 3 y - z = 7$ is
$2^i + 3^j -^k$
so the direction ratios of normal to plane are
$< 2, 3, - 1 >$

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A straight line passes through (1, -2, 3) and perpendicular to the plane 2x+3y−z=7.Find the direction ratios of normal to plane.

The correct option is A <2,3,−1>concept: for any planeax+by+cz+d=0,normal vector to this plane isa^i+b^j+c^kthe normal vector of the plane 2x+3y−z=7 is 2^i+3^j−^kso the direction ratios of normal to plane are<2,3,−1>

A straight line passes through (1, -2, 3) and perpendicular to the plane $2 x + 3 y - z = 7$ .Find the direction ratios of normal to plane.

The correct option is A $< 2, 3, - 1 >$
$concept: for any plane a x + b y + c z + d = 0, normal vector to this plane is a^i + b^j + c^k$
the normal vector of the plane $2 x + 3 y - z = 7$ is
$2^i + 3^j -^k$
so the direction ratios of normal to plane are
$< 2, 3, - 1 >$