A) \[5\mathbf{i}+\mathbf{j}-\mathbf{k}\]
B) \[5\mathbf{i}+3\mathbf{j}-3\mathbf{k}\]
C) \[2\mathbf{i}+\mathbf{j}+2\mathbf{k}\]
D) \[5\mathbf{i}+\mathbf{j}+\mathbf{k}\]
E) \[4\mathbf{i}+2\mathbf{j}-2\mathbf{k}\]
Correct Answer: B
Solution :
The point of the given line is \[(1+t,-1+t,1-t)\] Equation of plane is, \[x+y+z=5\] The point of the given line satisfies the equation of plane \[\therefore \]\[(1+t)(-1+t)+(1-t)=5\] Þ \[1+t=5\] Þ \[t=4\] \ Points are \[(5,\,\,3,\,-3)\] Hence, position vector of point is, \[5\mathbf{i}+3\mathbf{j}-3\mathbf{k}\].
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