Question
यदि दो सदिशों $2 \hat{i}+4 \hat{j}-5 \hat{k}$ तथा $-\lambda \hat{i}+2 \hat{j}+3 \hat{k}$ के योग पर सदिश $\hat{i}+2 \hat{j}+\hat{k}$ का प्रक्षेप 1 है, तो $\lambda$ बराबर है ...............
$\vec{b}=(2-\lambda) \hat{i}+6 \hat{j}-2 \hat{k}$
$\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}=1, \vec{a} \cdot \vec{b}=12-\lambda$
$(\vec{a} \cdot \vec{b})=|\vec{b}|^{2}$
$\lambda^{2}-24 \lambda+144=\lambda^{2}-4 \lambda+4+40$
$20 \lambda=100 \Rightarrow \lambda=5$
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