JEE Main 2022 · 24 Jun · Shift 1 · Mathematics Q24

← JEE Main 2022 · 24 Jun · Shift 1

MathematicsInteger+4 / -1Question 24 of 90

Let a line having direction ratios $1,-4,2$ intersect the lines $\dfrac{x-7}3=\dfrac{y-1}{-1}=\dfrac{z+2}1$ and $\dfrac x2=\dfrac{y-7}3=\dfrac z1$ at the points $A$ and $B$ . Then $(AB)^2$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 84

General points. $A=(7+3s,1-s,-2+s)$ and $B=(2t,7+3t,t)$ .

Parallel to $(1,-4,2)$ . $B-A=(2t-7-3s,\ 6+3t+s,\ t+2-s)=k(1,-4,2)$ .

From the 1st and 3rd components: $t+2-s=2(2t-7-3s)$ , i.e. $3t=16+5s$ . From the 1st and 2nd: $6+3t+s=-4(2t-7-3s)$ , i.e. $t=2+s$ . So $s=-5$ , $t=-3$ .

Points. $A=(-8,6,-7)$ , $B=(-6,-2,-3)$ , $B-A=(2,-8,4)$ .

Value. $(AB)^2=4+64+16=84$ .

Answer: 84

Topics:Equation of a line in space Angles and distances

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JEE Main 2022 · 24 Jun · Shift 1, Mathematics question 24