# Consider the vector v between (-4,-4,-4) and (6,7,1).  The vector v is? The length of vector v is?

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should use the following notations for the given points `(-4,-4,-4)` and `(6,7,1)` , such that:

`A(x_A,y_A,z_A) = (-4,-4,-4)`

`B(x_B,y_B,z_B) = (6,7,1)`

You may write the vector ` bar (AB) = bar v` , such that:

`bar v = (x_B - x_A) bar i + (y_B - y_A) bar j + (z_B - z_A) bar k`

Making the substitutions yields:

`bar v = (6 - (-4)) bar i + (7 - (-4)) bar j + (1 - (-4)) bar k`

`bar v = 10 bar i + 11 bar j + 5 bar k`

You may evaluate the length of the vector, such that:

`|bar v| = sqrt((x_B - x_A)^2 + (y_B - y_A)^2 +(z_B - z_A)^2)`

`|bar v| = sqrt(10^2 + 11^2 + 5^2)`

`|bar v| = sqrt(100 + 121 + 25) = sqrt246 ~~15.68`

Hence, evaluating the vector `bar v `  yields `bar v = 10 bar i + 11 bar j + 5 bar k` and evaluating the length of the vector` bar v = sqrt 246` .

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