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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $\vec a = 2\hat i + \hat j - 2\hat k,; \vec b = \hat i + \hat j$ and $\vec c = \vec a \times \vec b$.
Let $\vec d$ be a vector such that $|\vec d - \vec a| = \sqrt{11},; |\vec c \times \vec d| = 3$ and the angle between $\vec c$ and $\vec d$ is $\frac{\pi}{4}$. Then $\vec a \cdot \vec d$ is equal to:
Solution
$\vec c = 2\hat i + 2\hat k + \hat k = 2\hat i + 2\hat j + \hat k$
$|\vec c| = 3$
$|\vec c \times \vec d| = |\vec c||\vec d|\sin\frac{\pi}{4}$
$3 = 3|\vec d|\cdot \frac{1}{\sqrt{2}} \Rightarrow |\vec d| = \sqrt{2}$
$|\vec d - \vec a|^2 = |\vec d|^2 + |\vec a|^2 - 2\vec a\cdot\vec d$
$11 = 2 + 9 - 2\vec a\cdot\vec d$
$\Rightarrow \vec a\cdot\vec d = 0$
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