Question

1.Two vectors A and B of magnitude 5 units and 7 units respectively make an angle 60° with each other as shown below. Find the magnitude of the resultant vector and its direction with respect to 7 unit the vector A .​

Answer 1

Answer:

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Answer 2

Answer:

The value of resultant vector is √109 and its angle with 7 unit vector is β=24.22°.

Explanation:

Given are the magnitudes of vector A and vector B to be 7 and 5 units and angle between(α) them to be 60°.

Resultant vector is evaluated by the formula,

$R_{eq} =\sqrt{A^{2} +B^{2}+2ABcos\alpha }$

where A and B are magnitudes of the given vector and $\alpha$ is the angle between the 2 vectors.

Substituting the values of A, B and α we get,

$R_{eq} =\sqrt{7^{2} +5^{2}+2*7*5cos 60 }\\R_{eq} =\sqrt{109}$

Magnitude of the resultant vector is √109.

Angle between the resultant and given vector (β) is given by the relation,

$\beta =tan^{-1} (\frac{Bsin\alpha }{A+Bcos\alpha } )$

$\beta =tan^{-1} (\frac{5sin60 }{7+5cos60 } )$

On solving for β, we get

β=24.22°

Hence, The value of resultant vector is √109 and its angle with 7 unit vector is β=24.22°.