If ∣ a ∣ = 4 , ∣ b ∣ = 2 and the angle between a and b is π /6 then ( a × b ) 2 = 2 is equal to

We have, a ⋅ b = ∣ a ∣∣ b ∣ cos 6 π = 4 × 2 × 2 3 = 4 3 Now, ( a × b ) 2 + ( a ⋅ b ) 2 = a 2 b 2 ⇒ ( a × b ) 2 + 48 = 16 × 4 ⇒ ( a × b ) 2 = 16

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MathematicsVectorDot Product & Its Application ( Projection etc.)Easy2 minPYQ_2002

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If $∣ a ∣ = 4, ∣ b ∣ = 2$ and the angle between $a$ and $b$ is $π /6$ then $(a \times b)^{2} = 2$ is equal to

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We have, $a \cdot b = ∣ a ∣∣ b ∣ cos \frac{π}{6} = 4 \times 2 \times \frac{3}{2} = 43$ Now, $(a \times b)^{2} + (a \cdot b)^{2} = a^{2} b^{2} \Rightarrow (a \times b)^{2} + 48 = 16 \times 4 \Rightarrow (a \times b)^{2} = 16$

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

⏱ 2mℹ️ Source: PYQ_2002

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