Question

What is the purpose of Cross Multiplication?

Answer 1

Cross Multiplication

• The purpose of cross multiplication is to simplify an equation involving ratios to find any unknown variables.

For example, for the equation $\frac{20}{a}=\frac{2}{3}$, the value of $a$ need to be determined. The numerator of the LHS is multiplied with the denominator of the RHS and the numerator of the RHS is multiplied with the denominator of the LHS.

We get, $20\times 3=2\times a$

Now the value of $a$ can be found by dividing the equation by $2$

$\Rightarrow a=\frac{20\times 3}{2}$

$\Rightarrow a=30$

Cross multiplication in vector:

The cross multiplication of two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$gives the vector which is perpendicular to the plane made by the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$.

To find the perpendicular vector, we use cross multiplication.

The cross multiplication of $\overrightarrow{a}=x_{1}i+y_{1}j+z_{1}k$ and $\overrightarrow{b}=x_{2}i+y_{2}j+z_{2}k$ is

$\left[\begin{array}{ccc}i& j& k\\ x_1& y_1& z_1\\ x_2& y_2& z_2\end{array}\right]$