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3-1.Vectors
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સદીશ $A=\hat{i}+\hat{j}+\hat{k}$ નો સદીશ $\vec{B}=\hat{i}+\hat{j}$ પરનો પ્રક્ષેપણ શું થાય?
A
$\sqrt{2}(\hat{i}+\hat{j})$
B
$(\hat{i}+\hat{j})$
C
$\sqrt{2}(\hat{i}+\hat{j}+\hat{k})$
D
$2(\hat{i}+\hat{j}+\hat{k})$
(JEE MAIN-2021)
Solution
Projection of vector $A$ on vector $B$
$(A \cos \theta) \hat{B}=A\left(\frac{\bar{A} \cdot \bar{B}}{A B}\right) \hat{B}=\frac{\bar{A} \cdot \bar{B}}{B} \hat{B}$
$=\frac{2}{\sqrt{2}}\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)=\hat{i}+\hat{j}$
Standard 11
Physics
