Math, asked by Anubhavsingh8599, 11 months ago

If a and b are two unit vectors the what is the angle between a and b so that √3a-b be a unit vector

Answers

Answered by MaheswariS
7

\textbf{Given:}

\text{$\overrightarrow{a}$ , $\overrightarrow{b}$ and $\sqrt{3}\overrightarrow{a}-\overrightarrow{b}$ are unit vectors}

\text{Then,$|\overrightarrow{a}|$=$|\overrightarrow{b}|$=$|\sqrt{3}\overrightarrow{a}-\overrightarrow{b}|$=1}

\implies|\sqrt{3}\overrightarrow{a}-\overrightarrow{b}|^2=1^2}

\text{We know that,}

\boxed{\bf|\overrightarrow{a}-\overrightarrow{b}|^2=|\overrightarrow{a}|^2+|\overrightarrow{b}|^2-2\,|\overrightarrow{a}|\,|\overrightarrow{b}|\,cos\theta}

\implies\,3|\overrightarrow{a}|^2+|\overrightarrow{b}|^2-2\sqrt{3}\,|\overrightarrow{a}|\,|\overrightarrow{b}|\,cos\theta=1

\implies\,3(1)^2+(1)^2-2\sqrt{3}(1)(1)cos\theta=1

\implies\,4-2\sqrt{3}cos\theta=1

\implies\,2\sqrt{3}cos\theta=3

\implies\,2cos\theta=\sqrt{3}

\implies\,cos\theta=\frac{\sqrt{3}}{2}

\implies\boxed{\bf\theta=\frac{\pi}{6}}

\therefore\textbf{The angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\pi}{6}$}

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If |a| = 13,|b|= 5 and a.b = 60, then

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