2D vector geometry calculator
28 Feb
Sick And Tired Of Doing 2D VECTOR GEOMETRY The Old Way? Read This

 

2D Vector Problems Solved using Calcuhubs Calculator App

A 2D Vector is a vector geometry in 2-dimensions and can be calculated by taking the square root of the sum of each components in space.

\dpi{100} \LARGE \cos\theta=\frac{\left(\overrightarrow{a\ \ }.\ \ \overrightarrow{b}\right)}{\left|\overrightarrow{a}\right|\ \ \left|\overrightarrow{b}\right|}

Formula of Angle Between 2D Vectors

\dpi{100} \LARGE \theta=\cos^{-1}\left[\frac{\left(x_a\times x_b\right)+\left(y_a\times y_b\right)}{\left(\sqrt{\left(\left(x_a\right)^2+\left(x_b\right)^2\right)}\right)\times\sqrt{\left(\left(y_a\right)^2+\left(y_b\right)^2\right)}}\right]

 

Problem 1. Angle Between Two Vectors

Solve the angle between these two vectors  \dpi{100} \LARGE a\left(12,\ 7\right),\ b\left(5,\ 6\right).

Solution

\dpi{100} \LARGE \left(\overrightarrow{a\ \ }.\ \ \overrightarrow{b}\right)

\dpi{100} \LARGE a.b=\sum_{i=1}^na_ib_i=a_1b_1+a_2b_2+...+a_nb_n

\dpi{100} \large a.b=\sum_{i=1}^na_ib_i=a_i=12,\ b_i=5,a_j=7,\ b_j=6

\dpi{100} \LARGE (12\times5)+(7\times6)

\dpi{100} \LARGE (60)+(42)=102

\dpi{100} \large \dpi{100} \LARGE \cos\theta=\frac{102}{\sqrt{\left(12^2+7^2\right)\times\left(5^2+6^2\right)}}

\dpi{100} \large \dpi{100} \LARGE \cos\theta=\frac{102}{\sqrt{\left(144+49\right)\times\left(25+36\right)}}

\dpi{100} \large \dpi{100} \LARGE \cos\theta=\frac{102}{\sqrt{\left(193\right)\times\left(61\right)}}

\dpi{100} \large \dpi{100} \LARGE \cos\theta=\frac{102}{\sqrt{\left(11773\right)}}

\dpi{100} \LARGE \theta=\cos^{-1}\left(\frac{102}{108.5034}\right)

Representing vector result in degree

\dpi{100} \LARGE \theta=\cos^{-1}\left(0.94\right)

\dpi{100} \huge \theta=19.938^{\degree}

Representing vector result in radians, first convert the degree to radian as shown below

\dpi{100} \LARGE 1^{\degree}\times\frac{\pi}{180}=1Rad

Since you have 19.938 degree, then in radians will be

\dpi{100} \LARGE 19.938^{\degree}\times\frac{\pi}{180}

\dpi{100} \LARGE 19.938^{\degree}\times\frac{3.142}{180}

\dpi{100} \LARGE 19.938^{\degree}\times0.0174555556

\dpi{100} \huge = 0.3480 Radians

For more or to solve unlimited 2D Vector geometry problems, download Calcuhubs Calculators on Google Playstore for free.