Cosine of the angle between the lines l r=5 i-j+4 k+ (i+2 j+2 k) … - Vidyadip

MCQ

Cosine of the angle between the lines
$\begin{array}{l} \bar{r}=5 \hat{i}-\hat{j}+4 \hat{k}+\lambda(\hat{i}+2 \hat{j}+2 \hat{k}) \text { and } \\ \bar{r}=7 \hat{i}+2 \hat{j}+2 \hat{k}+\mu(3 \hat{i}+2 \hat{j}+6 \hat{k}) \text { is } \end{array}$

A
$0$
B
$\frac{1}{2}$
✓
$\frac{19}{21}$
D
$\frac{1}{3}$

✓

Answer

Correct option: C.

$\frac{19}{21}$

(C)
$a_1, b_1, c_1=1,2,2$ and $a_2, b_2, c_2=3,2,6$
$\therefore \quad \cos \theta=\left|\frac{1 \times 3+2 \times 2+2 \times 6}{\sqrt{1^2+2^2+2^2} \sqrt{3^2+2^2+6^2}}\right|$
$=\frac{19}{3 \times 7}=\frac{19}{21}$

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