If ( a × b ) 2 + ( a ⋅ b ) 2 = 676 and ∣ b ∣ = 2 then ∣ a ∣ is equal to

( a × b ) 2 + ( a ⋅ b ) 2 = 676 ( ∣ a ∣ ⋅ ∣ b ∣ sin θ n ^ ) 2 + ( ∣ a ∣ ⋅ ∣ b ∣ cos θ ) 2 = 676 ⇒ a 2 b 2 sin 2 θ + a 2 b 2 cos 2 θ = 676 [ ( n ^ ) 2 = 1 ] a 2 b 2 ( sin 2 θ + cos 2 θ ) = 676 ⇒ a 2 = b 2 676 = 4 676 ∣ a ∣ = 4 676 ⇒ ∣ a ∣ = 2 26 ⇒ ∣ a ∣ = 13

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MathematicsVectorDot Product & Its Application ( Projection etc.)Easy2 minPYQ_2010

MathematicsEasysingle choice

If $(a \times b)^{2} + (a \cdot b)^{2} = 676$ and $∣ b ∣ = 2$ then $∣ a ∣$ is equal to

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$(a \times b)^{2} + (a \cdot b)^{2} = 676 (∣ a ∣ \cdot ∣ b ∣ sin θ \overset{n}{^})^{2} + (∣ a ∣ \cdot ∣ b ∣ cos θ)^{2} = 676 \Rightarrow a^{2} b^{2} sin^{2} θ + a^{2} b^{2} cos^{2} θ = 676 [(\overset{n}{^})^{2} = 1] a^{2} b^{2} (sin^{2} θ + cos^{2} θ) = 676 \Rightarrow a^{2} = \frac{676}{b ^{2}} = \frac{676}{4} ∣ a ∣ = \frac{676}{4} \Rightarrow ∣ a ∣ = \frac{26}{2} \Rightarrow ∣ a ∣ = 13$

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

⏱ 2mℹ️ Source: PYQ_2010

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