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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The vectors $\vec{a},\vec{b},\vec{c}$ are equal in length and taken pairwise make equal angles.
If $\vec{a}=\hat{i}+\hat{j}$, $\vec{b}=\hat{j}+\hat{k}$ and $\vec{c}$ makes an obtuse angle with $\hat{i}$, then $\vec{c}$ is equal to
Solution
Equal lengths and equal pairwise angles ⇒ vectors form a symmetric set. Dot-products must satisfy: $\vec{a}\cdot\vec{b}=\vec{b}\cdot\vec{c}=\vec{c}\cdot\vec{a}$ Also $\vec{c}$ must make obtuse angle with $\hat{i}$ ⇒ its $i$-component < 0. Solving gives: $\vec{c}=\frac{1}{3}\hat{i}+\frac{4}{3}\hat{j}-\frac{1}{3}\hat{k}$Online Test Series, Information About Examination,
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