Question:medium
Let
\[
\vec{a}
=
(\sin^2\alpha)\hat{i}
+
(\cos 2\alpha)\hat{j}
+
(\cos^2\alpha)\hat{k},
\qquad
0\leq\alpha\leq\frac{\pi}{2},
\]
and
\[
\vec{b}
=
\hat{i}
-
2\hat{j}
+
\hat{k}.
\]
If \(\vec{a}\) and \(\vec{b}\) are perpendicular to each other, then the value of \(\alpha\) is equal to:
Let
\[
\vec{a}
=
(\sin^2\alpha)\hat{i}
+
(\cos 2\alpha)\hat{j}
+
(\cos^2\alpha)\hat{k},
\qquad
0\leq\alpha\leq\frac{\pi}{2},
\]
and
\[
\vec{b}
=
\hat{i}
-
2\hat{j}
+
\hat{k}.
\]
If \(\vec{a}\) and \(\vec{b}\) are perpendicular to each other, then the value of \(\alpha\) is equal to:
Show Hint
Recognizing that \(\sin^2 \alpha + \cos^2 \alpha = 1\) immediately simplifies the dot product equation. Always look for fundamental identities in trigonometric vector problems.
Updated On: Jun 25, 2026
- \(\frac{\pi}{6}\)
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{3}\)
- \(\frac{\pi}{2}\)
- 0
Show Solution
The Correct Option is A
Solution and Explanation
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