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Question
The line of intersection of planes →r.(^i+^j+^k)=3 and →r.(2^i+3^j+^k)=9 is perpendicular to plane →r.(a^i+b^j+4^k)=5, then value of a+b is equal to
The line of intersection of planes →r.(^i+^j+^k)=3 and →r.(2^i+3^j+^k)=9 is perpendicular to plane →r.(a^i+b^j+4^k)=5, then value of a+b is equal to
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Solution
The correct option is A −4
Line of intersection of given planes is along the intersection of their normals.∣∣
∣
∣∣^i^j^k111231∣∣
∣
∣∣=^i(1−3)+^j(2−1)+^k(3−2)=−2^i+^j+^kNow, this is perpendicular to third plane, so the normal of third plane is parallel to the intersection line.⇒a−2=b1=41⇒a=−8,b=4
⇒a+b=−4Hence, option B is correct.
Line of intersection of given planes is along the intersection of their normals.
∣∣
∣
∣∣^i^j^k111231∣∣
∣
∣∣=^i(1−3)+^j(2−1)+^k(3−2)=−2^i+^j+^k
Now, this is perpendicular to third plane, so the normal of third plane is parallel to the intersection line.
⇒a−2=b1=41
⇒a=−8,b=4
⇒a+b=−4
Hence, option B is correct.
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and which is perpendicular to the plane
.