If ${ˆ a}_{1}, {ˆ a}_{2} and {ˆ a}_{3}$ $hata_1,hata_2andhata_3$ are unit vectors and $2 {ˆ a}_{1} + 2 {ˆ a}_{2} + {ˆ a}_{3} = 0$ $2hata_1+2hata_2+hata_3=0$ then angle between ${ˆ a}_{1} and {ˆ a}_{2}$ $hata_1 and hata_2$ is?

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If ${ˆ a}_{1}, {ˆ a}_{2} and {ˆ a}_{3}$ $hata_1,hata_2andhata_3$ are unit vectors and $2 {ˆ a}_{1} + 2 {ˆ a}_{2} + {ˆ a}_{3} = 0$ $2hata_1+2hata_2+hata_3=0$ then angle between ${ˆ a}_{1} and {ˆ a}_{2}$ $hata_1 and hata_2$ is?

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Answer 1 · 2018-06-23T08:06:17

${cos}^{- 1} (- \frac{7}{8}) \approx 151^{\circ}$ $cos^-1(-7/8) ~~ 151^circ$

Explanation:

${ˆ a}_{3} = - 2 ({ˆ a}_{1} + {ˆ a}_{2}) \Rightarrow$ $hat a_3 = -2( hat a_1+hat a_2) implies$
${ˆ a}_{3}^{2} = 4 {({ˆ a}_{1} + {ˆ a}_{2})}_{1}^{2}$ $hat a_3^2 =4 (hat a_1+hat a_2)^2$
$qquad = 4 (hat a_1^2+hat a_2^2+2 hat a_1 cdot hat a_2) implies$
$1 = 4(1+1 +2 hat a_1 cdot hat a_2 ) implies$
$hat a_1 cdot hat a_2 = -7/8$

Thus, the angle $theta$ between $hat a_1$ and $hat a_2$ is given by

$cos theta = (hat a_1 cdot hat a_2)/(|hat a_1| \ |hat a_2|)= -7/8$ and thus

$theta = cos^-1(-7/8) ~~ 151^circ$

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If ${ˆ a}_{1}, {ˆ a}_{2} and {ˆ a}_{3}$ $hata_1,hata_2andhata_3$ are unit vectors and $2 {ˆ a}_{1} + 2 {ˆ a}_{2} + {ˆ a}_{3} = 0$ $2hata_1+2hata_2+hata_3=0$ then angle between ${ˆ a}_{1} and {ˆ a}_{2}$ $hata_1 and hata_2$ is?

answer wrt sinh

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Explanation:

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If hata_1,hata_2andhata_3 ˆa1,ˆa2andˆa3hata_1,hata_2andhata_3 are unit vectors and2hata_1+2hata_2+hata_3=02ˆa1+2ˆa2+ˆa3=02hata_1+2hata_2+hata_3=0 then angle between hata_1 and hata_2 ˆa1andˆa2hata_1 and hata_2 is?

answer wrt sinh

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Explanation:

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If ${ˆ a}_{1}, {ˆ a}_{2} and {ˆ a}_{3}$ $hata_1,hata_2andhata_3$ are unit vectors and $2 {ˆ a}_{1} + 2 {ˆ a}_{2} + {ˆ a}_{3} = 0$ $2hata_1+2hata_2+hata_3=0$ then angle between ${ˆ a}_{1} and {ˆ a}_{2}$ $hata_1 and hata_2$ is?