If the points with position vectors α i + 10j + 13k, 6i + 11j + 1… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 8 April, Shift 1Cross Product

If the points with position vectors $\alpha \hat{i} + 10\hat{j} + 13\hat{k}$ , $6\hat{i} + 11\hat{j} + 11\hat{k}$ , and $\frac{9}{2}\hat{i} + \beta\hat{j} - 8\hat{k}$ are collinear, then $(19\alpha - 6\beta)^2$ is equal to:

A
$49$
B
$36$
C
$25$
D
$16$

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