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The direction ratios of a normal to the plane through (1, 0, 0), (0, 1, 0), which makes an angle of π/4 with the plane x + y = 3 are
  • a)
    < 1, √2, 1 >
  • b)
    < 1, 1, √2 >
  • c)
    < 1, 1, 2 >
  • d)
    < √2, 1, 1 >
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The direction ratios of a normal to the plane through (1, 0, 0), (0, 1...
A normal vector to a plane is perpendicular to the plane. Therefore, the direction ratios of a normal vector to the plane can be found by taking the cross product of the direction vectors of any two non-parallel vectors in the plane.

Let's take the two given points (1, 0, 0) and (0, 1, 0) and find their direction vectors:

Direction vector 1 = (1, 0, 0) - (0, 1, 0) = (1, -1, 0)
Direction vector 2 = (0, 1, 0) - (1, 0, 0) = (-1, 1, 0)

Now, we can find the cross product of these direction vectors to get the direction ratios of the normal vector.

Cross product = (1 * 1 - (-1) * 1, -1 * 0 - 1 * (-1), 1 * 1 - (-1) * 1) = (2, 1, 0)

Therefore, the direction ratios of a normal vector to the plane through (1, 0, 0) and (0, 1, 0) are (2, 1, 0).
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