Vector calculator

This calculator performs all vector operations. You can add, subtract, find length, find dot and cross product, check if vectors are dependent. For every operation, calculator will generate a detailed explanation.

Vectors in 2 dimensions
Six operations with two dimensional vectors + steps.
show help ↓↓ examples ↓↓
Magnitude (length) of $ V_1 $
$ v_1 + v_2 $ $ v_1 - v_2 $
$ v_1 \cdot v_2 $ - dot product Angle between $ v_1 $ and $ v_2 $
Check if $ v_1 $ and $ v_2 $ are linearly dependent
Find approximate solution
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Vectors in 3 dimensions
Seven operations with three dimensional vectors + steps.
show help ↓↓ examples ↓↓
Magnitude (length) of $ V_1 $
$ v_1 + v_2 $ $ v_1 - v_2 $
$ v_1 \cdot v_2 $ - dot product $ v_1 \cdot v_2 $ - cross product
angle between $ v_1 $ and $ v_2 $
Check if $ v_1 $, $ v_2 $ and $ v_3 $ are linearly dependent
Find approximate solution
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examples
example 1:ex 1:
Given vector $v_1 = (8, -4)$, calculate the the magnitude.
example 2:ex 2:
Calculate the difference of vectors $v_1 = \left(\frac{3}{4}, 2\right)$ and $v_2 = (3, -2)$.
example 3:ex 3:
Calculate the dot product of vectors $v_1 = \left(-\frac{1}{4}, \frac{2}{5}\right)$ and $v_2 = \left(-5, -\frac{5}{4}\right)$.
example 4:ex 4:
Find the angle between the vectors $v_1 = (3, 5, −7)$ and $v_2 = (-3, 4, -2)$.
example 5:ex 5:
Find the cross product of $v_1 = (-2, \frac{2}{3}, −3)$ and $v_2 = (4, 0, -\frac{1}{2})$.
example 6:ex 6:
Determine if the following set of vectors is linearly independent: $v_1 = (3, -2, 4)$ , $v_2 = (1, -2, 3)$ and $v_3 = (3, 2, -1)$.

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