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3-1.Vectors
easy
સદિશ $\mathop A\limits^ \to \,\, = \,\,\hat i\,\, + \;\,\hat j\,\, + \;\,\sqrt 2 \hat k$ અને $Z$ અક્ષ વચ્ચેનો ખૂણો ....... $^o$ શોધો .
A
$0$
B
$45$
C
$60$
D
$90$
Solution
Given
Lets,
$\vec{A} =\hat{i}+\hat{j}+\sqrt{2} \hat{k}$
$\vec{B}(z-\text { axis }) =\hat{k}$
We know formula
$\vec{A} \cdot \vec{B}=|\vec{A}||\vec{B}| \cos \theta$
$\cos \theta=\frac{\vec{A} \cdot \vec{B}}{|\vec{A}||\vec{B}|}=\frac{(0+0+\sqrt{2})}{\left(\sqrt{1^2+1^2+\sqrt{2}^2}\right) \cdot \sqrt{1^2}}$
$=\frac{\sqrt{2}}{\sqrt{4}}=\frac{1}{\sqrt{2}}$
$\cos \theta =\frac{1}{\sqrt{2}}$
$\theta =\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)=45^{\circ}$
Standard 11
Physics
