JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=\hat{i}-2 \hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}-\hat{j}+\hat{k}\) be two vectors. If \(\overrightarrow{\mathrm{c}}\) is a vector such that \(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}=0,\) then \(\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{b}}\) is equal to
- A \(\frac{1}{2}\)
- B \(-1\)
- C \(-\frac{1}{2}\)
- D \(-\frac{3}{2}\)
Answer & Solution
Correct Answer
(C) \(-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{a}}=\overrightarrow{0}\) \(\overrightarrow{\mathrm{b}} \times(\overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{a}})=\overrightarrow{0}\)…
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