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Question
The cartesian equation of the plane perpendicular to vector 3¯i−2¯j−2¯k and passing through the point 2¯i+3¯j−¯k is
The cartesian equation of the plane perpendicular to vector 3¯i−2¯j−2¯k and passing through the point 2¯i+3¯j−¯k is
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Solution
The correct option is D 3x−2y−2z=2
(→r−→a).→N=0⇒→a=2^i+3^j−^k⇒→N=3^i−2^j−2^k⇒(→r−2^i−3^j+^k).(3^i−2^j−2^k)=0⇒→r=x^i+y^j+^k⇒{(x−2)i+(y−3)^j+(z+1)^k}.(3i−2^j−2^k)=0⇒3(x−2)−2(y−3)−2(z+1)=0⇒3x−6−2y+6−2z−2=03x−2y−2z=2Ans.
(→r−→a).→N=0⇒→a=2^i+3^j−^k⇒→N=3^i−2^j−2^k⇒(→r−2^i−3^j+^k).(3^i−2^j−2^k)=0⇒→r=x^i+y^j+^k⇒{(x−2)i+(y−3)^j+(z+1)^k}.(3i−2^j−2^k)=0⇒3(x−2)−2(y−3)−2(z+1)=0⇒3x−6−2y+6−2z−2=03x−2y−2z=2Ans.
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