Question

Find the resultant vector
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Answer 1

Answer:

Answer is R(1+√2)

Explanation:

OR=OR

OA vector is along OB vector (bisector) and magnitude is 2R cos 45 = R√2

(OA vector + OC vector)+OB vector is along OB vector and its magnitude is

Rroot2+R = which is equal to the answer i mentioned above ..

Answer 2

Answer:

$R_{res} =R$

Explanation:

According to the figure,

magnitude of $R_{x} = R$

magnitude of $R_{y} =R$

Vector representation of $R_{x}$ and $R_{y}$ are Rcosθ and Rsinθ respectively.

Angle, θ = $45^{o}$

Since, rectangular components of the vector R are given in the question, we can find out the resultant vector, $R_{res}$ as:

                        $R_{res} = \sqrt{R_{x} ^{2} +R_{y} ^{2} }$

                        $R_{res} = \sqrt{R^{2} (cos 45^{o}) ^{2} +R ^{2} (sin 45^{o})^{2} }$

Taking common term,

                        $R_{res} = \sqrt{R^{2} [(cos 45^{o}) ^{2} +(sin 45^{o})^{2}] }$

Since $cos^{2} x + sin^{2} x = 1$, using the identity, we obtain

                        $R_{res} = \sqrt{R^2 } = R$

Hence, resultant is R itself.