Question

IF P.Q=√3 (magnitude of PxQ), then the angle between vector A and B is
(1) 45°
(2) 30°
(3) 60°
(4) 90°
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Answer 1

Your answer is :-

Given, P.Q = √3

as we know

P.Q = PQcos∅

•°• PQcos∅ = √3 ...(1)

also give

|P×Q| = √3

=> PQsin∅ = √3 (as we know P×Q = PQsin∅) ......(2)

from (1) & (2)

PQcos ∅= PQsin∅

=> tan∅ = 1

=> ∅ = 45°

Answer 2

Answer:

Angle between both vectors is 45°

Step-by-step explanation:

Given, P.Q = √3

As we know, dot product of two vectors is P.Q= |P||Q| cosθ

∴ |P||Q| cosθ= √3 .......(1)

Where θ is angle between both vectors P and Q.

Also given |P×Q| = √3

As we know, dot product of two vectors is  P×Q = |P||Q| sinθ

|P||Q| sinθ = √3  .........(2)

from equation (1) & (2)

|P||Q| cosθ = |P||Q| sinθ

tanθ = 1

θ = 45°

∴Angle between both vectors is 45°