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Two points P and Q in space have the co-...

Two points P and Q in space have the co-ordinates (2,4,4) and (-2,-3,7) respectively. What is the magnitude of the vector `vec PQ` ?

A

`sqrt(50)` units

B

`sqrt(62)` units

C

`sqrt(74)` units

D

`sqrt(91)` units

Text Solution

Verified by Experts

The correct Answer is:
C

Let O be the origin of the co-ordinate system. Then the position vectors of P and Q are given by
`vec (OP) = 2hati + 4hatj + 4hatk and vec (OQ) =-2 hati - 3hatj + 7 hatk`
From the figure, we find that
`vec (OP) + vec (PQ) = vec (OQ)`
`therefore vec (PQ) = vec (OQ) - vec (OP)`
`=(-2 hati - 3hatj + 7hatk) -(2hati+4hatj + 4hatk)`
`vec (PQ) =-4hati -7hatj + 3 hatk`
`therefore |vec (PQ)| = sqrt ((-4)^(2) + (-7)^(2) + (3)^(2))`
`=sqrt(16 + 49 +9) = sqrt (74)`
`therefore` Magnitude of `vec (PQ) = sqrt (74)` units
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