Find the vector equation of a plane which is at a distance of 7 units from the origin and which is normal to the vector $3 straight i with hat on top space plus space 5 space straight j with hat on top space minus space 6 space straight k with hat on top.$

Solution

Here p = 7
and $straight n with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space 5 space straight j with hat on top space minus space 6 space straight k with hat on top$
$therefore$ $straight n with hat on top space equals space fraction numerator straight n with rightwards arrow on top over denominator open vertical bar straight n with rightwards arrow on top close vertical bar end fraction space equals space fraction numerator 3 space straight i with hat on top space plus space 5 space straight j with hat on top space minus space 6 space straight k with hat on top over denominator square root of 9 plus 25 plus 36 end root end fraction space equals space fraction numerator 1 over denominator square root of 70 end fraction left parenthesis 3 space straight i with hat on top space plus space 5 space straight j with hat on top space minus space 6 space straight k with hat on top right parenthesis$
The vector equation of plane is
$straight r with rightwards arrow on top. space straight n with hat on top space equals space straight p$
or $straight r with rightwards arrow on top. space open parentheses fraction numerator 3 space straight i with hat on top space plus space 5 space straight j with hat on top space minus space 6 space straight k with hat on top over denominator space square root of 70 end fraction close parentheses space equals space 7.$

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Three Dimensional Geometry

Find the vector equation of a plane which is at a distance of 7 units from the origin and which is normal to the vector $3 straight i with hat on top space plus space 5 space straight j with hat on top space minus space 6 space straight k with hat on top.$

Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin²α + sin² β + sin²γ = 2.

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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Three Dimensional Geometry

Find the vector equation of a plane which is at a distance of 7 units from the origin and which is normal to the vector

Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin2α + sin2 β + sin2γ = 2.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the vector equation of a plane which is at a distance of 7 units from the origin and which is normal to the vector $3 straight i with hat on top space plus space 5 space straight j with hat on top space minus space 6 space straight k with hat on top.$

If α, β, γ are the angles which a line makes with the axes, prove that sin²α + sin² β + sin²γ = 2.