Question

Find the vector drown for the points (-4, 10, 7) to the point (3,-2,1). Also find its
magnitude.​

Answer 1

To find:

The vector drawn for the points (-4, 10, 7) to the point (3,-2,1) and its magnitude.

Calculation:

The vector joining the following points

• (-4 , 10 , 7)

• (3 , -2 , 1 )

will be :

$\therefore\: \vec{r} = \{3 - ( - 4) \}( \hat{i}) + \{ - 2 - 10 \}( \hat{j}) + \{1 - 7 \} ( \hat{k})$

$= > \vec{r} = \{3 + 4 \}( \hat{i}) + \{ - 12 \}( \hat{j}) + \{ - 6\} ( \hat{k})$

$= > \vec{r} = \{7\}( \hat{i}) + \{ - 12 \}( \hat{j}) + \{ - 6\} ( \hat{k})$

$\boxed{= > \vec{r} = 7( \hat{i}) - 12( \hat{j}) - 6( \hat{k})}$

So, magnitude of the vector :

$\therefore \: | \vec{r}| = \sqrt{ {7}^{2} + {( - 12)}^{2} + {( - 6)}^{2} }$

$= > \: | \vec{r}| = \sqrt{ 49 + 144 + 36 }$

$= > \: | \vec{r}| = \sqrt{ 229 }$

$\boxed{ = > \: | \vec{r}| = 15.13 \: units}$

Hope It Helps.