Discussion
Let \(\vec{a} = 6\hat{i} + 2\hat{j} + 3\hat{k}\). If \(\vec{b}\) is parallel to \(\vec{a}\) and \(\vec{a} . \vec{b}\) =\(\frac{49}{2}\), then \(|\vec{b}|\)=
Answer: E
\(|\vec{b}| = \) \(\frac{7}{2}\).
Being parallel, \(\vec{b} = k\vec{a}\). Since \(|\vec{a}| = \sqrt{36 + 4 + 9} = 7\):
\[ \begin{aligned} \vec{a}\cdot\vec{b} &= k|\vec{a}|^{2} = 49k = \frac{49}{2} \\ k &= \frac{1}{2},\quad |\vec{b}| = \frac{1}{2}(7) = \frac{7}{2} \end{aligned} \]
7 is \(|\vec{a}|\) itself, 49 is \(|\vec{a}|^{2}\), and 14 doubles instead of halving.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development