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Question: Given that \(\overset{\rightarrow}{A} + \overset{\rightarrow}{B} + \overset{\rightarrow}{C}\) = 0, o...

Given that A→+B→+C→\overset{\rightarrow}{A} + \overset{\rightarrow}{B} + \overset{\rightarrow}{C} = 0, out of three vectors two are equal in magnitude and the magnitude of third vector is 2\sqrt{2} times that of either of the two having equal magnitude. Then the angles between vectors are given by –

A

300,600,90030^{0},60^{0},90^{0}

B

450,450,90045^{0},45^{0},90^{0}

C

450,600,90045^{0},60^{0},90^{0}

D

900,1350,135090^{0},135^{0},135^{0}

Answer

900,1350,135090^{0},135^{0},135^{0}

Explanation

Solution

Let ∣A→∣=∣B→∣|\overrightarrow{A}| = |\overrightarrow{B}| = a and ∣C→∣=2a|\overrightarrow{C}| = \sqrt{2}a

then, A→+B→+C→\overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C} = 0 ̃ C→=−(A→+B→)\overrightarrow{C} = - (\overrightarrow{A} + \overrightarrow{B})

̃ C2 = A2 + B2 + 2AB cosq

̃ 2a2 = a2 + a2 + 2a2 cosq

̃ cos q = 0 ̃ q = 900