The line x - 1 1 = y - 2 - 2 = z - 1 3 and the plane x + 2 y + z = 6 meet at:

Question

The line $\frac{x - 1}{1} = \frac{y - 2}{- 2} = \frac{z - 1}{3}$ and the plane $x + 2 y + z = 6$ meet at:

Smart Achievers · Accepted Answer

(3)

Ans. infinitely many points

Explanation:

Direction ratios of given line are 1, -2, 3 and the d.r. of normal to the given plane are 1, 2, 1.

Since 1 × 1 + (-2) × 2 + 3 × 1 = 0, therefore, the line is parallel to the plane.

Also, the base point of the line (1, 2, 1) lies in the given plane.

(1 + 2 × 2 + 1 = 6 is true)

Hence, the given line lies in the given plane.

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