SATHEE: Kinematics Question 43

Kinematics Question 43

Question: Assertion : If q be the angle between $\vec{A}$ and $\vec{B}$ , then $\tan θ = \frac{\vec{A} \times \vec{B}}{\vec{A} . \vec{B}}$ Reason : $\vec{A} \times \vec{B}$ is perpendicular to $\vec{A} . \vec{B}$

Options:

A) If both assertion and reason are true and the reason is the correct explanation of the assertion.

B) If both assertion and reason are true but reason is not the correct explanation of the assertion.

C) If assertion is true but reason is false.

D) If the assertion and reason both are false.

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Answer:

Correct Answer: D

Solution:

$\frac{\vec{A} \times \vec{B}}{\vec{A} . \vec{B}} = \frac{A B \sin θ \hat{n}}{A B \cos θ} = \tan θ \hat{n}$ where $\hat{n}$ it’s unit vector perpendicular to both $\vec{A}$ and $\vec{B}$ . However $\frac{| \vec{A} \times \vec{B} |}{\vec{A} . \vec{B}} = \tan θ$

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Kinematics Question 43

Question: Assertion : If q be the angle between A→ and B→ , then tan⁡θ=A→×B→A→.B→ Reason : A→×B→ is perpendicular to A→.B→

Options:

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Question: Assertion : If q be the angle between $\vec{A}$ and $\vec{B}$ , then $\tan θ = \frac{\vec{A} \times \vec{B}}{\vec{A} . \vec{B}}$ Reason : $\vec{A} \times \vec{B}$ is perpendicular to $\vec{A} . \vec{B}$