Question

A mosquito flies from a point A(-1,2,3)m to a point B(2,-1,-2)m . The displacement of the mosquito is

Answer 1

A mosquito flies from a point A(-1,2,3)m to a point B(2,-1,-2)m . The displacement of the mosquito is

Explanation:

We have-

Initial position vector, \overrightarrow{r1} = -\hat{i} + 2\hat{j} + 3\hat{k}

Final position vector, \overrightarrow{r2} = 2\hat{i} - \hat{j} - 2\hat{k}

Displacement vector of the mosquito \overrightarrow{r} is given by-

\overrightarrow{r} = \overrightarrow{r2} - \overrightarrow{r1}

So, we have-

\overrightarrow{r} = (2\hat{i} - \hat{j} - 2\hat{k})-(-\hat{i} + 2\hat{j} + 3\hat{k})

\overrightarrow{r} = 3\hat{i} - 3\hat{j} - 5\hat{k}

Thus, displacement vector of the mosquito is-

{\color{DarkRed}\mathbf{\overrightarrow{r} = 3\hat{i} -3\hat{j} - 5\hat{k}}}

The magnitude of displacement is given by-

|\overrightarrow{r}|

= √(32 + 32 + 52)

= √(9 + 9 + 25)

= √43 m

Answer 2

Explanation:

Here i cap ,j cap and k cap are the ar to gonal unit vectors

a bar equals to (-1) iCAP + 2 j cap + 3 k cap

B bar equals to minus ICAP + 2j cap + 3 k cap

B bar equals to 2i cap minus 1 j cap - 2 k cap

displacement s equals to b bar minus a bar

(2i cap-j cap- k cap)-(-i cap+2j cap+ 3k cap)

= 3i cap-3 j cap-5k cap