A vector A makes an angle of 20° and B makes an angleof 110° with th

1.	A vector A makes an angle of 20° and B makes an angleof 110° with the X-axis. The magnitudes of these vectorsare 3 m and 4 m respectively. Find the resultant.
Answer» From the above figure, we have:Angle between →A and →B = 110° − 20° = 90°∣∣∣→A∣∣∣=3 m and ∣∣∣→B∣∣∣= 4 m Magnitude of the resultant vector is given byR=√A2+B2+2AB cos θ =√32+42+2×3×4×cos 90° = 5 m Let β be the angle between →R and →A.β=tan−1 (A sin 90°A+B cos 90°) =tan−1 (4 sin 90°3+4 cos 90°) =tan−1 43 =tan−1 (1.333) =53° Now, angle made by the resultant vector with the X-axis = 53° + 20° = 73°∴ The resultant →R is 5 m and it makes an angle of 73° with the x-axis.

A vector A makes an angle of 20° and B makes an angleof 110° with the X-axis. The magnitudes of these vectorsare 3 m and 4 m respectively. Find the resultant.

Answer»

From the above figure, we have:Angle between →A and →B = 110° − 20° = 90°∣∣∣→A∣∣∣=3 m and ∣∣∣→B∣∣∣= 4 m

Magnitude of the resultant vector is given byR=√A2+B2+2AB cos θ =√32+42+2×3×4×cos 90° = 5 m

Let β be the angle between →R and →A.β=tan−1 (A sin 90°A+B cos 90°) =tan−1 (4 sin 90°3+4 cos 90°) =tan−1 43 =tan−1 (1.333) =53°

Now, angle made by the resultant vector with the X-axis = 53° + 20° = 73°∴ The resultant →R is 5 m and it makes an angle of 73° with the x-axis.

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A vector A makes an angle of 20° and B makes an angleof 110° with the X-axis. The magnitudes of these vectorsare 3 m and 4 m respectively. Find the resultant.

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