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Question

If n is a vector of magnitude 3 and is equally inclined with an acute angle with the coordinate axes. Find the vector and cartesian forms of equation of a plane which passes through (2,1,1) and is normal to n.

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Solution

Let α,β,γ angles of ¯n
Given angels are equal So: α=β=γ
ie: cosα=cosβ=cosγ
So direction cosines l=m=nl=l=l
As we know l2+m2+n2=n8l2=1
l=1/3
Given magnitude =3
¯n=3(13^i+13^j+13^k)=^i+^j+^k
Given (2,1,1)¯a=2^i+^j+^k & ¯n=^i+^j+^k
get plane equation ¯r.n=¯a.¯n
¯r(^i+^j+^k)=(2^i+^j^k)(^i+^j+^k)
=2+11
¯r(^i+^j+^k)=2
(x^i+y^j+z^k)(^i+^j+^k)=2 [¯r=x^i+y^j+z^k]
x+y+z=2 As we want Question form

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