IIT-JEE 2008 · Paper 2 · Mathematics Q17

MathematicsSingle correct+4 / -1Question 17 of 66

Passage

Paragraph for Question Nos. 17 to 19

Consider the lines
$L_1:\frac{x+1}3=\frac{y+2}1=\frac{z+1}2,\qquad L_2:\frac{x-2}1=\frac{y+2}2=\frac{z-3}3.$

The unit vector perpendicular to both $L_1$ and $L_2$ is

\dfrac{-\hat i+7\hat j+7\hat k}{\sqrt{99}}

\dfrac{-\hat i-7\hat j+5\hat k}{5\sqrt3}

\dfrac{-\hat i+7\hat j+5\hat k}{5\sqrt3}

\dfrac{7\hat i-7\hat j-\hat k}{\sqrt{99}}

Answer and worked solution

Official answer: B

Cross product of the directions.
$(3,1,2)\times(1,2,3)=(3-4,\ 2-9,\ 6-1)=(-1,-7,5),\qquad|(-1,-7,5)|=\sqrt{75}=5\sqrt3.$

(B) $\dfrac{-\hat i-7\hat j+5\hat k}{5\sqrt3}$

IIT-JEE 2008 · Paper 2, Mathematics question 17