Vector calculator

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

Vectors in 2 dimensions
Six operations with two dimensional vectors + steps.
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Magnitude (length) of V1
Sum of V1 and V2 Difference of V1 and V2
Scalar (dot) product of V1 and V2 Angle between V1 and V2
Determine if V1 and V2 are linearly independent or linearly dependent
Find approximate solution
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Vectors in 3 dimensions
Seven operations with three dimensional vectors + steps.
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magnitude (length) of V1
sum of V1 and V2 difference of V1 and V2
scalar (dot) product of V1 and V2 cross product of V1 and V2
angle between V1 and V2
Check if V1, V2 and V3 are linearly dependant
Find approximate solution
Hide steps
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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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