Question

plz anyone give me correct answer I will give you brainliest ​

Answer 1

Answer :-

Vectors are :-

$\hat{i}+\hat{j}$

$\hat{i}+\hat{k}$

To find :-

$Angle\;b/w\;the\;vectors.$

Solution :-

Let the vectors be $\overrightarrow{a}=\hat{i}+\hat{j}$ and $\overrightarrow{b}=\hat{i}+\hat{k}$.

Angle b/w these vectors is given by :-

$cos\theta = \dfrac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{a}||\overrightarrow{b}|}$

Finding $\overrightarrow{|a|}$ :-

› √(1)² + (1)²

› √1 + 1

› √2

Finding $\overrightarrow{|b|}$ :-

› √(1)² + (1)²

› √1 + 1

› √2

Now, ${\overrightarrow a}.{\overrightarrow b}$ :-

$\hat{i}+\hat{j}$ . $\hat{i}+\hat{k}$

›  (1)(1) + (1)(0) + (1)(0)

› 1

$Now\; cos\theta =\dfrac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{a}||\overrightarrow{b}|}$

› $\dfrac{1}{\sqrt{2}.\sqrt{2} }$

› $\dfrac{1}{2}$

› $\; cos\theta = \dfrac{1}{2}$

∴ The value of $\theta$ is 60°