Dot Product

Q. A particle moves with a velocity, $\overrightarrow{v}=(5\hat{i}-3\hat{j}+6\hat{k})\text{m/s}$ at an instant, under the influence of a constant force, $\overrightarrow{F}=(10\hat{i}+10\hat{j}+20\hat{k})\text{N}$. The instantaneous power applied to the particle is

1. $110\text{W}$
2. $120\text{W}$
3. $140\text{W}$
4. $150\text{W}$

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

Considering two vectors $\overrightarrow{A}=\hat{i}+2\hat{j}$ and $\overrightarrow{B}=2\hat{i}+\hat{j}$. Choose the correct statement(s).

दो सदिश $\overrightarrow{A}=\hat{i}+2\hat{j}$ तथा $\overrightarrow{B}=2\hat{i}+\hat{j}$ पर विचार करते हुए, सही कथन/कथनों का चयन कीजिए।

1. Angle between $(\overrightarrow{A}+\overrightarrow{B})$ and $(\overrightarrow{A}-\overrightarrow{B})$ is 90°
   
   $(\overrightarrow{A}+\overrightarrow{B})$ व $(\overrightarrow{A}-\overrightarrow{B})$ के मध्य कोण 90° है S
2. $(\overrightarrow{A}+\overrightarrow{B})\cdot \overrightarrow{A}=9$
3. $\left|(\overrightarrow{A}-\overrightarrow{B})\times \overrightarrow{A}\right|=(\overrightarrow{A}+\overrightarrow{B})\cdot \overrightarrow{A}$
4. $(\overrightarrow{A}\cdot \overrightarrow{B})=2$