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MathematicsVectorDot Product & Its Application ( Projection etc.)Easy2 minPYQ_2012

MathematicsEasysingle choice

Let $\overset{a}{^}$ and $\hat{b}$ be two unit vectors. If the vectors $c = \overset{a}{^} + 2 \hat{b}$ and $d = 5 \overset{a}{^} - 4 \hat{b}$ are perpendicular to each other, then the angle between $\overset{a}{^}$ and $\hat{b}$ is

Options:

Answer:

C

Solution:

$c \cdot d = 0 \Rightarrow 5∣ a ∣^{2} + 6 a \cdot b - 8∣ b ∣^{2} = 0$ $\Rightarrow 6 a \cdot b = 3 \Rightarrow a \cdot b = \frac{1}{2} \Rightarrow (a \cdot b) = \frac{π}{3}$

Stream:JEESubject:MathematicsTopic:VectorSubtopic:Dot Product & Its Application ( Projection etc.)

⏱ 2mℹ️ Source: PYQ_2012

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