SATHEE: Kinematics Question 601

Kinematics Question 601

Question: If $| \vec{a} | = 4, | \vec{b} | = 2$ and the angle between $\vec{a}$ and $\vec{b}$ it’s $π / 6$ then ${(\vec{a} \times \vec{b})}^{2}$ is equal to

Options:

A) 48

B)16

C) 4

D)2

Show Answer

Answer:

Correct Answer: B

Solution:

[b] We have, $\vec{a} . \vec{b} = | \vec{a} | | \vec{b} | c o s \frac{π}{6}$

$= 4 \times 2 \times \frac{\sqrt{3}}{2} = 4 \sqrt{3} .$

Now ${(\vec{a} \times \vec{b})}^{2} + {(\vec{a} . \vec{b})}^{2} = a^{2} b^{2};$

$\Rightarrow {(\vec{a} \times \vec{b})}^{2} + 48 = 16 \times 4 \Rightarrow {(\vec{a} \times \vec{b})}^{2} = 16$

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Kinematics Question 601

Question: If |a→|=4,|b→|=2 and the angle between a→ and b→ it’s π/6 then (a→×b→)2 is equal to

Options:

Answer:

Solution:

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Question: If $| \vec{a} | = 4, | \vec{b} | = 2$ and the angle between $\vec{a}$ and $\vec{b}$ it’s $π / 6$ then ${(\vec{a} \times \vec{b})}^{2}$ is equal to