Adding, subtracting, and multiplying vectors Quiz 1

Question 1

If $$	heta  $$ is the angle between $$\overrightarrow{a}=4\hat{i}-2\hat{j}+\hat{k}$$ and $$\overrightarrow{b}=2\hat{i}+\hat{j}-2\hat{k}$$ and $$\cos 	heta =\dfrac{p}{q\sqrt{21}}$$, then find the value of $$p+q$$.

Accepted Answer

7

Answer

3

Answer

4

Answer

5

Question 2

$$\overrightarrow{a},\overrightarrow{b}$$ and $$\overrightarrow{c}$$ are unit vectors such that $$2\overrightarrow{a}+3\overrightarrow{b}+4\overrightarrow{c}=0$$ and the angle between $$\overrightarrow{a}$$ and $$\overrightarrow{b}$$ is $$	heta $$, find value of $$\left( 4\cos 	heta -1 ight)$$

Accepted Answer

0

Answer

1

Answer

-1

Answer

2

Question 3

If $$\vec{a}=3\hat{i}+2\hat{j}-6\hat{k}$$ and $$\vec{b}=\hat{j}+4\hat{i}-2\hat{k}$$ then find the value of $$3\left( -\vec{a} \right)+4\left( {\vec{b}} \right)$$

Accepted Answer

$$7\hat{i}-2\hat{j}+10\hat{k}$$

Answer

0

Answer

$$7\hat{i}+2\hat{j}-10\hat{k}$$

Answer

$$7\hat{i}-10\hat{j}-10\hat{k}$$

Question 4

If $$\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$$ are mutually perpendicular vectors of magnitude 1,2,3 units respectively . Find the value of $$\left[ 2\overrightarrow{b}-\overrightarrow{c}	ext{   2}\overrightarrow{c}-\overrightarrow{a}	ext{  2}\overrightarrow{a}-\overrightarrow{b} ight]$$.

Accepted Answer

42

Answer

6

Answer

36

Answer

18

Question 5

Let $$I$$ be the incentre of a $$\Delta ABC$$ where $$\dfrac{\overrightarrow{BC}}{\left| \overrightarrow{BC} \right|}+\dfrac{\overrightarrow{BA}}{\left| \overrightarrow{BC} \right|}=\dfrac{\overrightarrow{BI}}{k}$$, and are unit vectors , then the diameter of the circumcircle of triangle is

Accepted Answer

$$k\left( \cot \dfrac{A}{2}+\cot \dfrac{C}{2} \right)$$

Answer

$$\left( \cot \dfrac{A}{2}+\cot \dfrac{C}{2} \right)$$

Answer

$$\left( \cot \dfrac{A}{2}-\cot \dfrac{C}{2} \right)$$

Answer

$$k\left( \cot \dfrac{A}{2}-\cot \dfrac{C}{2} \right)$$