SATHEE: Kinematics Question 442

Kinematics Question 442

Question: The value of $\hat{i} \times (\hat{i} \times \vec{a}) + \hat{j} \times (\hat{j} + \vec{a}) + \hat{k} + (\hat{k} \times \hat{a})$ it’s

Options:

A) $\vec{a}$

B) $\vec{a} \times \hat{k}$

C) $- 2 \vec{a}$

D) $- \vec{a}$

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Suppose $\vec{a} = a_{1} \hat{i} + a_{2} \hat{j} + a_{3} \hat{k}$

Now, $(\hat{i} \times \vec{a}) = a_{2} \hat{k} - a_{3} \hat{j}$

Now, $\hat{i} \times (\hat{i} \times \vec{a}) = - a_{2} \hat{j} - a_{2} \hat{k}$

Similarly, $\hat{j} \times (\hat{j} \times \vec{a}) = - a_{1} i 6 - a_{3} \hat{k}$

and $\hat{k} \times (\hat{k} \times \vec{a}) = - a_{1} \hat{i} - a_{2} \hat{j}$

$∴$ $\hat{i} \times (\hat{i} \times \vec{a}) + \hat{j} \times (\hat{j} \times \vec{a}) + \vec{k} \times (\hat{k} \times \vec{a}) = - 2 \vec{a} .$

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Kinematics Question 442

Question: The value of i^×(i^×a→)+j^×(j^+a→)+k^+(k^×a^) it’s

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Question: The value of $\hat{i} \times (\hat{i} \times \vec{a}) + \hat{j} \times (\hat{j} + \vec{a}) + \hat{k} + (\hat{k} \times \hat{a})$ it’s