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Q.

The resultant of two vectors A=5i^ and B is R. The direction of R is such that it makes an angle π6 with the positive x - axis in anticlockwise sence. Find the magnitude of R(in cm) when B has minimum magnitude.( Take 3=1.732 )

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answer is 4.

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Detailed Solution

given α=300 resultant makes an angle 300 with P

tanα=B sinθA+B cosθ=13

3Bsinθ=A+Bcosθ

B3sinθ-cosθ=A

B=A3sinθ-cosθ

B=A232sinθ-12cosθ

B=A2sinθ-30

for B should be minimum θ-30=90 θ=1200

 

From triangle R=5cos300=532
 

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The resultant of two vectors A→=5i^ and B→ is R→. The direction of R→ is such that it makes an angle π6 with the positive x - axis in anticlockwise sence. Find the magnitude of R→(in cm) when B→ has minimum magnitude.( Take 3=1.732 )