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  • If the points with position vectors  <img alt="\alpha \hat{i}+10 \hat{j}+13 \hat{k}, 6 \hat{i}+11 \hat{j}+11 \hat{k}, \frac{9}{2} \hat{i}+\beta \hat{j}-8 \hat{k}" src="https://entrancecorner.o

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

Option: 1

49


Option: 2

36


Option: 3

25


Option: 4

16


Answers (1)

best_answer

\begin{aligned} & (\alpha, 10,13) ;(6,11,11),\left(\frac{9}{2}, \beta,-8\right) \\ & \frac{\alpha-6}{3 / 2}=\frac{-1}{11-\beta}=\frac{2}{19} \\ & \alpha-6=\frac{3}{19} & -19=22-2 \beta \\ & \alpha=6+\frac{3}{19}=\frac{117}{19} & 2 \beta=41 \\ & \therefore(19 \alpha-6 \beta)^2=(117-123)^2=36 \\ & \end{aligned}

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Kuldeep Maurya

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