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3-1.Vectors
medium
If $\vec A = 2\hat i + \hat j - \hat k,\,\vec B = \hat i + 2\hat j + 3\hat k$ and $\vec C = 6\hat i - 2j - 6\hat k$ then the angle between $(\vec A + \vec B)$ and $\vec C$ wil be ....... $^o$
A
$30$
B
$45$
C
$60$
D
$90$
Solution
$\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{D}}$
$\overrightarrow{\mathrm{D}}=3 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}$
$\overrightarrow{\mathrm{C}}=6 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}$
$\overrightarrow{\mathrm{D}} \cdot \overrightarrow{\mathrm{C}}=18-6-12=0$
$\theta=90^{\circ}$
Standard 11
Physics
