JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec a\, = \,\hat i\, + \,2\hat j\, + 4\hat k\,,\,\vec b\, = \,\hat i\, + \,\lambda \hat j\, + 4\hat k\) and \(\vec c\, = \,2\hat i\, + \,4\hat j\, + ({\lambda ^2} - 1)\hat k\) be coplanar vectors. Then the non -zero vector \(\vec a\times \vec c\) is
- A \( - 10\,\,\hat i\, - 5\,j\)
- B \( - 14\,\,\hat i\, - 5\,j\)
- C \( - 14\,\,\hat i\, + 5\,j\)
- D \( - 10\,\,\hat i\, + 5\,j\)
Answer & Solution
Correct Answer
(D) \( - 10\,\,\hat i\, + 5\,j\)
Step-by-step Solution
Detailed explanation
\(\left[\begin{array}{lll}{\vec{a}} & {\vec{b}} & {\vec{c}}\end{array}\right]=0\) \(\left|\begin{array}{lll}{1} & {2} & {4} \\ {1} & {\lambda} & {4} \\ {2} & {4} & {\lambda^{2}-1}\end{array}\right|_{R_{3} \rightarrow R_{3}-2 R_{1}}=0\)…
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