JEE Mains · Maths · STD 12 - 10. vector algebra
Let \( \vec{a}=-\hat{i}+2\hat{j}+2\hat{k}, \) \( \vec{b}=8\hat{i}+7\hat{j}-3\hat{k} \) and \( \vec{c} \) be a vector such that \( \vec{a}\times\vec{c}=\vec{b} \). If \( \vec{c}.(\hat{i}+\hat{j}+\hat{k})=4, \) then \( |\vec{a}+\vec{c}|^{2} \) is equal to:
- A 33
- B 27
- C 35
- D 30
Answer & Solution
Correct Answer
(B) 27
Step-by-step Solution
Detailed explanation
\( \hat{a}=-\hat{i}+2\hat{j}+2\hat{k} \) \( \vec{b}=8\hat{i}+7\hat{j}-3\hat{k} \) \( \vec{c}=c_{1}\hat{i}+c_{2}\hat{j}+c_{3}\hat{k} \) \( \vec{a}\times\vec{c}=\vec{b}\Rightarrow(2c_{3}-2c_{2})\hat{i}+(c_{3}+2c_{1})\hat{j}-(c_{2}+2c_{1})\hat{k}=8\hat{i}+7\hat{j}-3\hat{k} \)…
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