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Question

Equation of a plane passing through ^i+^j+^k parallel to both ^i+^j and ^j+^k can be given by


A

¯r.(^i+^j+^k)=1

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B

¯r.(^i^j+^k)=1

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C

¯r.(^i+^j^k)=1

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D

¯r.(^i^j^k)=1

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Solution

The correct option is B

¯r.(^i^j+^k)=1


We know equation of plane passing through ¯a perpendicular to ^nis (r¯a).^n=0
Here, a=^i+^j+^k
How to get ^n?

We can see ^n is perpendicular to both ^i+^j and ^j+^k i.e., along (^i+^j)×(^j+^k).

(^i+^j)×(^j+^k)=∣ ∣ ∣^i^j^k110011∣ ∣ ∣=^i(1)^j(1)+^k(1)=^i^j+^k

^n=^i^j+^k12+12+12=^i^j+^k3 equation of plane(¯r(^i+^j+^k)).^n=0

¯r.(^i^j+^k3)=1212+123=13¯r.(^i^j+^k)=1


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