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Vectors

If a⃗, b⃗, ...

Question

If $\to a, \to b, \to c$ are three coplanar vectors then find the magnitude of their vector sum. It is given $\to a = 4^i -^j,$ $\to b = - 3^i + 2^j$ , $\to c = - 3^j$ .

A

\sqrt{5}, 297^{\circ}

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B

\sqrt{5}, 63^{\circ}

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C

\sqrt{3}, 297^{\circ}

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D

\sqrt{3}, 63^{\circ}

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Solution

The correct option is D $\sqrt{5}, 297^{\circ}$
Here, the vector sum , $\to R = \to a + \to b + \to c = (4^i -^j) + (- 3^i + 2^j) - 3^j =^i - 2^j$
So, $| \to R | = \sqrt{1^{2} + (- 2)^{2}} = \sqrt{5}$
As the sum vector is in x-y plane so $tan θ = y / x = - 2 / 1 = - 2$ or $θ = 297^{o}$

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