Mathematics - Vector Question with Solution | TestHub

MathematicsVectorGeneral definitions, Angle between vectors, Section formula, Geometrical resultsMedium2 minPYQ_2013

MathematicsMediumsingle choice

If $a, b, c$ are three unit vectors such that $a + b + c = 0,$ where $0$ is null vector, then $a \cdot b + b \cdot c + c \cdot a$ is :

Options:

Answer:

Solution:

We have $a + b + c = 0$ $∣ a + b + c ∣ = 0 \Rightarrow ∣ a + b + c ∣^{2} = 0$ $\Rightarrow ∣ a ∣^{2} + ∣ b ∣^{2} + ∣ c ∣^{2}$ $+ 2 (a \cdot b + b \cdot c + c \cdot a) = 0$ $\Rightarrow 1 + 1 + 1 + 2 (a \cdot b + b \cdot c + c \cdot a) = 0$ $\Rightarrow a \cdot b + \overset{ˉ}{b} \cdot c + \overset{c}{ˉ} \cdot \overset{a}{ˉ} = - \frac{3}{2}$

Stream:BITSATSubject:MathematicsTopic:VectorSubtopic:General definitions, Angle between vectors, Section formula, Geometrical results

⏱ 2mℹ️ Source: PYQ_2013

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