Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# If P(0, 1, 2), Q(4, –2, 1) and O(0, 0, 0) Are Three Points, Then ∠Poq = - Mathematics

MCQ

If P(0, 1, 2), Q(4, –2, 1) and O(0, 0, 0) are three points, then ∠POQ

#### Options

• $\frac{\pi}{6}$

•  $\frac{\pi}{4}$

• $\frac{\pi}{3}$

• $\frac{\pi}{2}$

#### Solution

$\frac{\pi}{2}$

$P Q^2 = \left( 4 - 0 \right)^2 + \left( - 2 - 1 \right)^2 + \left( 1 - 2 \right)^2 = 16 + 9 + 1 = 26$
$O P^2 = \left( 0 - 0 \right)^2 + \left( 1 - 0 \right)^2 + \left( 2 - 0 \right)^2 = 0 + 1 + 4 = 5$
$Q O^2 = \left( 0 - 4 \right)^2 + \left( 0 + 2 \right)^2 + \left( 0 - 1 \right)^2 = 16 + 1 + 4 = 21$
$Since, P Q^2 = O P^2 + Q O^2$
$Hence, ∠POQ = \frac{\pi}{2}$

Concept: Three Dimessional Space
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 28 Introduction to three dimensional coordinate geometry
Q 3 | Page 22