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Question

Write the equation of the line passing through (3,5,1) & which is parallel to the line formed by joining points (2,5,7) & (3,4,9).

A
r=(3,5,1)+λ(1,1,2)
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B
r=(1,1,2)+λ(3,5,1)
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C
r=(3,5,1)+λ(1,1,2)
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D
r=(1,1,2)+λ(3,5,1)
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Solution

The correct option is C
r=(3,5,1)+λ(1,1,2)

The line is parallel to the line formed by joining points A(2,5,7) and B(3,4,9)

Let a and b are the position vectors of points A and B

then
a=2^i+5^j+7^k
b=3^i+4^j+9^k

ba=^i^j+2^k


Now, the line passes through the point (3,5,1) and parallel to the vector
^i^j+2^k.

So, the position vector r of any point on the line is,
r=3^i+5^j+^k+λ(^i^j+2^k)











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