JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\vec a,\vec b\) and \(\vec c\) are unit vectors such that \(\vec a + 2\vec b + 2\vec c = \vec 0\), then \(\left| {\vec a \times \vec c} \right|\) is equal to
- A \(\frac{1}{{4}}\)
- B \(\frac{{\sqrt {15} }}{4}\)
- C \(\frac{15}{{16}}\)
- D \(\frac{{\sqrt {15} }}{16}\)
Answer & Solution
Correct Answer
(B) \(\frac{{\sqrt {15} }}{4}\)
Step-by-step Solution
Detailed explanation
(b) \(\quad \because \vec{a}+2 \vec{b}+2 \vec{c}=\overrightarrow{0}\) [Given] \(\Rightarrow \vec{a}+2 \overrightarrow{\mathrm{c}}=-2 \vec{b}\) \( \Rightarrow (\vec a + 2\vec c) \cdot (\vec a + 2\overrightarrow {\rm{c}} ) = ( - 2\vec b)( - 2\overrightarrow {\rm{b}} )\)…
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