If u ^ and v ^ are unit vectors and θ is the acute angle between them, then 2 u ^ × 3 v ^ is a unit vector for

∣2 u ^ × 3 v ^ ∣ = 1 6∣ u ^ ∥ v ^ ∥ sin θ ∣ = 1 sin θ = 6 1 Hence there is exactly one value of θ for which 2 u ^ × 3 v ^ is a unit vector.

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MathematicsVectorDot Product & Its Application ( Projection etc.)Easy2 minPYQ_2007

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If $\overset{u}{^}$ and $\overset{v}{^}$ are unit vectors and $θ$ is the acute angle between them, then $2 \overset{u}{^} \times 3 \overset{v}{^}$ is a unit vector for

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Solution:

$∣2 \overset{u}{^} \times 3 \overset{v}{^} ∣ = 1$ $6∣ \overset{u}{^} ∥ \overset{v}{^} ∥ sin θ ∣ = 1 sin θ = \frac{1}{6}$ Hence there is exactly one value of $θ$ for which $2 \overset{u}{^} \times 3 \overset{v}{^}$ is a unit vector.

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

⏱ 2mℹ️ Source: PYQ_2007

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