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Solution for If → a and → B Are Two Unit Vectors Such that → a + → B is Also a Unit Vector, Then Find the Angle Between → a and → B - CBSE (Commerce) Class 12 - Mathematics

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Question

If \[\vec{a}\] and \[\vec{b}\] are two unit vectors such that \[\vec{a} + \vec{b}\] is also a unit vector, then find the angle between \[\vec{a}\] and \[\vec{b}\] 

Solution

Let the angle between \[\vec{a}\] and \[\vec{b}\] be \[\theta\] It is given that \[\left| \vec{a} \right| = \left| \vec{b} \right| = \left| \vec{a} + \vec{b} \right| = 1\]  

\[\left| \vec{a} + \vec{b} \right| = 1\]

\[ \Rightarrow \left| \vec{a} + \vec{b} \right|^2 = 1\]

\[ \Rightarrow \left| \vec{a} \right|^2 + 2\left| \vec{a} \right|\left| \vec{b} \right|\cos\theta + \left| \vec{b} \right|^2 = 1\]

\[ \Rightarrow 1 + 2 \times 1 \times 1 \times \cos\theta + 1 = 1\]

\[ \Rightarrow 2\cos\theta = - 1\]

\[ \Rightarrow \cos\theta = - \frac{1}{2} = \cos\frac{2\pi}{3}\]

\[ \Rightarrow \theta = \frac{2\pi}{3}\] 

Thus, the angle between \[\vec{a}\] and \[\vec{b}\]  is \[\frac{2\pi}{3}\] 

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Solution If → a and → B Are Two Unit Vectors Such that → a + → B is Also a Unit Vector, Then Find the Angle Between → a and → B Concept: Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors.
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