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JEE Mains · Maths · STD 12 - 10. vector algebra

Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three units vectors such that \(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=\overrightarrow{0} .\) If \(\lambda=\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}} \) and \(\overrightarrow{\mathrm{d}}=\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{a}},\) then the ordered pair \((\lambda, {\mathrm{\vec d}})\) is equal to 

  1. A \(\left(-\frac{3}{2}, 3 \overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}\right)\)
  2. B \(\left(-\frac{3}{2}, 3 \overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{b}}\right)\)
  3. C \(\left(\frac{3}{2}, 3 \overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}\right)\)
  4. D \(\left(\frac{3}{2}, 3 \overline{\mathfrak{a}} \times \overline{\mathfrak{c}}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\left(-\frac{3}{2}, 3 \overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}\right)\)

Step-by-step Solution

Detailed explanation

\(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=\overrightarrow{0}\)…