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in 3D Coordinate Geometry by (49.9k points)
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If O be the origin and P (2, 3, 4) and Q (1, -2, 1) be any two points, show that OP ⊥ OQ.

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by (48.6k points)
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Best answer

It is given that

Line joining O (0, 0, 0) and P (2, 3, 4) is written as

OP = 2i + 3j + 4k

Line joining O (0, 0, 0) and Q (1, -2, 1) is written as

OQ = i – 2j + k

In order prove that these two lines are perpendicular we must show that angle between these two lines is π/2

Dot product

OP. OQ = 0

Substituting the values

(2i + 3j + 4k). (i – 2j + k) = 2 – 6 + 4 = 0

Therefore, it is proved that these two lines are perpendicular.

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