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Three Dimensional Geometry

Question
CBSEENMA12033355

Find a unit normal vector to the plane x + 2y + 3z – 6 = 0.

Solution
The equation of plane is x + 2y’ + 3z – 6 = 0
Direction-ratios of a normal to the plane are 1, 2, 3.
Dividing each by square root of left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared plus left parenthesis 3 right parenthesis squared end root space equals space square root of 14 comma the direction-cosines of a normal to the given plane are fraction numerator 1 over denominator square root of 14 end fraction comma space fraction numerator 2 over denominator square root of 14 end fraction comma space fraction numerator 3 over denominator square root of 14 end fraction
 ∴    the normal vector to the given plabne is fraction numerator 1 over denominator square root of 14 end fraction straight i with hat on top plus space fraction numerator 2 over denominator square root of 14 end fraction straight j with hat on top space plus space fraction numerator 3 over denominator square root of 14 end fraction straight k with hat on top.

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