Two vectors P and Q have magnitudes 3 units and 4 units respectively. Ř is the
resultant of P and Q. Find the magnitude and direction of Ř when the angle theta
between P and Q is 30°.
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Answer:
The magnitude of the resultant is given as,
R
2
=P
2
+Q
2
+2PQcosθ
R
2
=(3)
2
+(4)
2
+2×3×4cos30
∘
R=6.766units
Let the angle between the resultant and P is α.
The direction of resultant is given as,
tanα=
P+Qcosθ
Qsinθ
tanα=
4+3cos30
∘
4×sin30
∘
α=16.86
∘
Thus, the magnitude and direction of resultant is 6.766units and 16.86
∘
respectively.
Step-by-step explanation:
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