First slide

Scalars and Vectors

Question

Given that P=Q=R. If P+Q=R, then the angle between P and R is $θ_{1}$ . If P+Q+R=0, then the angle between P and R is $θ_{2}$ . What is the relation between $θ_{1}$ and $θ_{2}$ ?

Moderate

A

$θ_{1} = θ_{2}$
B

$θ_{1} = \frac{θ_{2}}{2}$
C

$θ_{1} = 2 θ_{2}$
D

None of these

Solution

$P + Q = R$ and P=Q=R
$R = \sqrt{P^{2} + Q^{2} + 2 P Q \cos θ}$
Substituting P=Q=R, we get $θ = 120 °$
If P=Q, then R will pass through the centre of P and Q. Hence, angle between P and R will be
$θ_{1} = \frac{θ}{2} = 60 °$
In the second condition, given that P=Q=R and $P + Q + R = 0$ . Then, angle between P and R will be $θ_{2} = 120 °$
$θ_{1} = \frac{θ_{2}}{2}$

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