Question

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

Answer 1

Magnitude =
`\sqrt({145)`.

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
`√(145)`

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=√(12^2+1^2)=√(144+1)=√(145)`

Hence, Magnitude of wx is
`√(145)`