Question

No spamming,Very important guys,Please solve this Find the angle between two vectors 2î +3j+k and -3i + 6k ,Answer is 90 degrees explain​

Answer 1

Answer:

electric field vector between the plates. In unit-vector notation, what uniform magnetic

Answer 2

Answer:

$\theta \: = {90}^{ \circ}$

Explanation:

Let,

$\sf \vec{a} = 2 \hat{i }+ 3 \hat{j }+ \hat{ k} \\ \sf \vec{b} = - 3 \hat{i }+ 6\hat{ k} \\ \\ \bigstar \: \green {\sf \: angle \: berween \: them \: \theta \: = \: to \: find}$

Now,

$\sf |\vec{a} | = \sqrt{ {2}^{2} + {3}^{2} + {1}^{2} } = \sqrt{14} \\ \sf |\vec{b} | = \sqrt{ {( - 3)}^{2} + {0}^{2} + {6}^{2} } = \sqrt{45} \\ \\ \sf\vec{a}. \vec{b} = (2 \hat{i }+ 3 \hat{j }+ \hat{ k}). (- 3 \hat{i }+ 6 \hat{ k}) \\ \sf \: \: \: \: \: \: = 2 \times ( - 3) + 3 \times 0 + 1 \times 6 \\ \: \: \: \: \: \: = - 6 + 0 + 6 \\ \: \: \: \: \: \: = 0$

We know that,

$\: \: \: \: \sf \vec{a}. \vec{b} = | \vec{a}| . | \vec{b}| cos \theta \\ \sf \implies \: cos \theta = \frac{\vec{a}. \vec{b}}{| \vec{a}| . | \vec{b}|} \\ \sf \implies \:\sf \: cos \theta = \frac{0}{ \sqrt{14} \times \sqrt{45} } = 0 \\ \sf \implies \: \ \: \theta = {cos}^{ - 1} 0 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \therefore \sf \theta = {90}^{ \circ}$

Short technique :

$\green{ \boxed{ \sf \: if \: \: \: \vec{a}. \vec{b} = 0 \: \: \: then \: \: \theta = {90}^{ \circ} } }\:$