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Question

The vector equation of the line of intersection of the planes r.(i+2j+3k)=0 and r.(3i+2j+k)=0 is

A
r=λ(i+2j+k)
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B
r=λ(i2j+k)
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C
r=λ(i+2j3k)
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D
None of these
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Solution

The correct option is A r=λ(i2j+k)
The line of intersection of the planes r.(i+2j+3k)=0 and r.(3i+2j+k)=0 is parallel to the vector
(i+2j+3k)×(3i+2j+k)=4i+8j4k
Since both the planes pass through the origin, therefore their line of intersection will also pass through the origin.
Thus, the required line passes through the origin and is parallel to the vector4i+8j4k
Hence, its equation is
r=0+λ(4i+8j4k)r=λ(i2j+k) where λ=4λ

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