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If \hat{u}\; \; and\; \; \hat{v} are unit vectors and \Theta  is the acute angle between them, then 2\hat{u} \times 3\hat{v} is a unit vector for

  • Option 1)

    no value of \Theta

  • Option 2)

    exactly one value of \Theta

  • Option 3)

    exactly two values of \Theta

  • Option 4)

    more than two values of  \Theta

 

Answers (1)

best_answer

As we have learned

Vector Product of two vectors(cross product) -

If \vec{a} and \vec{b} are two vectors and \Theta is the angle between them , then \vec{a}\times \vec{b}=\left |\vec{a} \left | \right |\vec{b} \right |Sin\Theta \hat{n}

- wherein

\hat{n} is unit vector perpendicular to both \vec{a} \: and \: \vec{b}

 

 

|2 \hat{u}\times 3\hat{v}| = 1

\Rightarrow 6 |\hat{u}\times \hat{v}| = 1 \\ \Rightarrow 6 |\sin \theta | = 1 \\ \Rightarrow |\sin \theta |= \pm 1/6

For acute angle \theta , one such angle is possible 

 

 

 

 

 


Option 1)

no value of \Theta

Option 2)

exactly one value of \Theta

Option 3)

exactly two values of \Theta

Option 4)

more than two values of  \Theta

Posted by

Himanshu

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