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Question

The cartesian equation of a line is 6x2=3y+2=2z2. Find its direction ratios & also find vector equation of the line.

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Solution

The cartesian equation of the line is
6x2=3y+2=2z2
6(x13)=3(y+23)=2(z1)x131=y+232=z13

p(13,23,1)

Direction ratios are (1,2,3)

Vector equation of the line is
r=13ˆi23ˆj+ˆk+λ(ˆi+2ˆj+3ˆk)


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