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If the line, (x − 3)/2 = (y + 2)/(−1) = (z + 4)/3 lies in the plane, lx + my − z = 9, then l² + m² is equal to:

1. 5
2. 2
3. 26
4. 18

Correct answer: 2

Solution

The line's direction ratios can be derived from the given equation, which are (2, -1, 3). For the line to lie in the plane, the normal vector of the plane must be orthogonal to the direction ratios of the line. The coefficients of x, y, and z in the plane equation give us the normal vector (l, m, -1). Solving the orthogonality condition leads to the conclusion that l² + m² equals 2.

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