If the magnitudes of the Vectors A,B, and
C are 6, 8, 10 units Respectively. and if Á + B = C
the the angle between A vector and C vector is
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Class 11
>>Physics
>>Motion in a Plane
>>Mathematical Operations on Vectors
>>If A = B + C and the magnitudes of A , B
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If A=B+C and the magnitudes of A,B and C are 5,4 and 3 units, the angle between A and C is
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Correct option is A)
Given:
A
=
B
+
C
A=5
B=4
C=3
∴
A
=
B
+
C
=
A
−
C
=
B
=
B
=
A
−
C
(a−b)
2
=a
2
+b
2
−2ab
=(4)
2
=(5)
2
+(3)
2
−2(5)(3)cosθ
=16=25+9−30cosθ
=16−34=−30cosθ
=18=−30cosθ
=cosθ=
−30
−18
=
5
3
=cosθ=
5
3
=θ=cos
−1
(3/5)
Hence,
option (A) is correct answer.
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