Let a line passing through the point $(-1, 2, 3)$ intersect the lines $L_1: \frac{x-1}{3} = \frac{y-2}{2} = \frac{z+1}{-2}$ at $M(\alpha, \beta, \gamma)$ and $L_2: \frac{x+2}{-3} = \frac{y-2}{-2} = \frac{z-1}{4}$ at $N(a, b, c)$. Then the value of $\frac{(\alpha + \beta + \gamma)^2}{(a + b + c)^2}$ equals ________.

JEE Main 2024 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 30 January 2024, Shift 2, Maths Q29

Question 29 of 90 in this shift, Maths question 29 of 30, Section B.

Let a line passing through the point

(-1, 2, 3)

intersect the lines

L_1: \frac{x-1}{3} = \frac{y-2}{2} = \frac{z+1}{-2}

M(\alpha, \beta, \gamma)

and

L_2: \frac{x+2}{-3} = \frac{y-2}{-2} = \frac{z-1}{4}

N(a, b, c)

. Then the value of

\frac{(\alpha + \beta + \gamma)^2}{(a + b + c)^2}

equals ________.

Official answer

196

NTA final key.