Question:medium
If
\[
\{(2,-3,5),\ (1,\alpha,7),\ (3,\beta,3)\}
\]
is not a basis of the vector space \(\mathbb{R}^3\), then \((\alpha,\beta)\) lies on the locus:
If
\[
\{(2,-3,5),\ (1,\alpha,7),\ (3,\beta,3)\}
\]
is not a basis of the vector space \(\mathbb{R}^3\), then \((\alpha,\beta)\) lies on the locus:
Show Hint
Whenever vectors are asked to form a basis of \(\mathbb R^3\), immediately construct a \(3\times3\) matrix and check its determinant. A zero determinant indicates linear dependence.
Updated On: Jun 25, 2026
- \(x^{2}+y=5\)
- \(y^{2}+x=4\)
- \(x+y+6=0\)
- \(x^{2}+y^{2}=16\)
Show Solution
The Correct Option is C
Solution and Explanation
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