Question

Find the magnitude of wx for w(-3 5 4) and x(9 5 3)

Answer 1

Answer:

Magnitude = $\sqrt({145)$.

Step-by-step explanation:

Given : wx for w(-3 5 4) and x(9 5 3).

To find : find the magnitude of wx .

Solution : We have given that w(-3 5 4) and x(9 5 3).

Magnitude = $\sqrt({x_{2} -x_{1} )^{2}+({y_{2} -y_{1} )^{2} +({z_{2} -z_{1})^{2}$.

$x_{1}= -3$ , $x_{2} = 9$ , $y_{1} = 5$ , $y_{2} = 5$, $z_{1} = 4$, $z_{2} = 3$.

Plugging the values in above formula ,

Magnitude = $\sqrt({9 - (-3))^{2}+({5-5 )^{2} +({3 -4)^{2}$.

Magnitude = $\sqrt({12)^{2}+({0 )^{2} +({-1^{2}$.

Magnitude = $\sqrt({144+0+1)$.

Magnitude = $\sqrt({145)$.

Therefore, Magnitude = $\sqrt({145)$.

Answer 2

Answer:  Magnitude of wx is $\sqrt{145}$

Step-by-step explanation:

Since we have given that

$w(-3,5,4)=-3\hat{i}+5\hat{j}+4\hat{k}\\\\x(9,5,3)=9\hat{i}+5\hat{j}+3\hat{k}$

Now, first we will find 'wx':

$wx=Initial-Final\\\\wx=(9+3)\hat{i}+(5-5)\hat{j}+(3-4)\hat{k}\\\\wx=12\hat{i}-1\hat{k}$

We need to find the "magnitude":

$\mid wx\mid=\sqrt{12^2+1^2}=\sqrt{144+1}=\sqrt{145}$

Hence, Magnitude of wx is $\sqrt{145}$