Let,, be the image of the point P(3, 3, 5) in the plane 2x + y - 3z = 6. Then + + is equal to:

Let,, be the image of the point P(3, 3, 5) in the plane 2x + y -… — Solution | JEE Mathematics

MCQMediumJEE 2023Equation of Plane

Let $\alpha, \beta, \gamma$ be the image of the point $P(3, 3, 5)$ in the plane $2x + y - 3z = 6$ . Then $\alpha + \beta + \gamma$ is equal to:

Correct answer:C

Standard Method

Given: The point is $P(3,3,5)$ and the plane is

2x + y - 3z = 6

Find: The value of $\alpha + \beta + \gamma$ , where $\left(\alpha,\beta,\gamma\right)$ is the image of the point in the plane.

The solution states that the image of a point in a plane is found using reflection across the plane. It gives the reflected point as

\alpha = 6, \quad \beta = 5, \quad \gamma = -1

Now add the coordinates:

\alpha + \beta + \gamma = 6 + 5 - 1 = 10

Therefore, the value of $\alpha + \beta + \gamma$ is $10$ . The correct option is C.

Using the plane coefficients incorrectly in the reflection formula is a common mistake. The normal vector must come from $2x + y - 3z - 6 = 0$ , so the coefficients are $2,1,-3$ . Use the complete plane equation in standard form before substituting.
Students often find the reflected coordinates correctly but forget that the question asks for $\alpha + \beta + \gamma$ , not the point itself. After obtaining the image point, add the three coordinates carefully.
Another mistake is substituting the point into the plane expression with sign errors, especially for the term $-3z$ . Preserve the negative sign while evaluating the expression to avoid an incorrect reflected point.

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