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3-1.Vectors
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The direction cosines of vector $( A - B )$, if $A =2 \hat{ i }+3 \hat{ j }+\hat{ k }, B =2 \hat{ i }+2 \hat{ j }+3 \hat{ k }$ are
A$0, \frac{1}{\sqrt{5}}, \frac{-2}{\sqrt{5}}$
B$0, \frac{2}{\sqrt{5}}, \frac{1}{\sqrt{5}}$
C$0,0, \frac{1}{\sqrt{5}}$
DNone of the above
Solution
(a)
$A – B =\hat{ j }-2 \hat{ k }= C$
$C =\sqrt{1+4}=\sqrt{5}$
$\cos \alpha=\frac{0}{\sqrt{5}}=0, \cos \beta=\frac{1}{\sqrt{5}}$
and $\cos \gamma=\frac{-2}{\sqrt{5}}$
$A – B =\hat{ j }-2 \hat{ k }= C$
$C =\sqrt{1+4}=\sqrt{5}$
$\cos \alpha=\frac{0}{\sqrt{5}}=0, \cos \beta=\frac{1}{\sqrt{5}}$
and $\cos \gamma=\frac{-2}{\sqrt{5}}$
Standard 11
Physics
