JEE Main 2022 · 27 Jun · Shift 1 · Mathematics Q30

← JEE Main 2022 · 27 Jun · Shift 1

MathematicsInteger+4 / -1Question 30 of 90

Let the mirror image of the point $(a,b,c)$ with respect to the plane $3x-4y+12z+19=0$ be $(a-6,\beta,\gamma)$ . If $a+b+c=5$ , then $7\beta-9\gamma$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 137

Reflection. The image is $(a,b,c)-2\lambda(3,-4,12)$ with $\lambda=\frac{3a-4b+12c+19}{169}$ ; the $x$ -shift $-6$ gives $\lambda=1$ .

So $\beta=b+8$ , $\gamma=c-24$ , and $3a-4b+12c=150$ . With $a=5-b-c$ : $-7b+9c=135$ .

Value. $7\beta-9\gamma=7b-9c+272=-135+272=137$ .

Answer: 137

Topics:Equation of a plane Angles and distances

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JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 30