Tamil Nadu Board of Secondary EducationHSC Science Class 11

# The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B. Then the angle between A and B is - Physics

MCQ
Sum

The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B. Then the angle between A and B is

• 30°

• 45°

• 150°

• 120°

#### Solution

Given:

The resultant of vecA & vecB is perpendicular to vecA and the magnitude of the resultant (C) = 1/2 vecB and α = 90°

Solution:

(i) Magnitude of resultant:

C^2 = A^2 + B^2 + 2AB costheta

B^2/4 = A^2 + B^2 + 2AB(A/B)

-3/4B^2 = 3A^2 ⇒ B^2 = 4A^2 i.e. B = 2A

(ii) direction of resultant:

tan α = (B sintheta)/(A + B costheta)

∞ = (Bsintheta)/(A + B costheta)

A + B cos θ = 0

cos θ = -"A"/"B" = -"A"/(2"A") = -1/2

cos θ = -1/2

θ = cos^-1(-1/2)

θ = 120°

Concept: Elementary Concept of Vector Algebra
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Chapter 2: Kinematics - Evaluation [Page 101]

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