Cross Product
Other than dot products, there is a different approach to multiplying two vectors together. Albeit the dot product of two vectors gives a scalar, in contrast, the resultant vector is a vector of cross-products. As so, its scale and direction are at the same time. Thus the cross product of the vectors is expressed in the magnitude and the angle as well of the two vectors and written as is expressed as
Both vectors are perpendicular to the direction of the cross product. The right-hand rule to acquire the appropriate orientation of cross product is used. Point your index finger (your right hand’s) in the first vector direction. Then align your hand to the second vector such that your middle finger points. Expand your thumb. The direction of your thumb indicates the cross-product direction.
For two vectors, we first need to guarantee both vectors are three-dimensional vectors in order to get the cross-product. If the two vectors are given in 3 dimensions, then the product is given as:
Calculating Cross Product
To calculate the Cross Product of two vectors, use standard unit vectors i, j, and k for R3.
If u = (u1, u2, u3) = u1i + u2j + u3k,
and v = (v1, v2, v3) = v1i + v2j + v3k,
then u × v is given as
u × v = (u2v3 − u3v2) i + (u3v1 − u1v3) j + (u1v2 − u2v1) k Rectangle Area
A four-sided polygon, in which each angle of each vertex is 90° and has the same lengths of the opposing sides, is known as a rectangle. Thus a 2-dimensional polygon form is a rectangle with four faces, four vertices, and four right angles. In the rectangle, the two sides opposite are parallel. The rectangular area is the space in the form. The area of the rectangle is also the perimeter of the rectangle. This differentiates the rectangle area from integration in which we calculate the area under the curve.
To calculate the area, in terms of shape, the rectangle is considered the easiest one. The area is the space covered by any form or item. However, descriptively we can say that an area is the quantity of a flat region bounded within a specific form. The typical area units often used include cm2 (centimeter square), m2 (meter square), and km2 (kilometer square).
How to Calculate Rectangle Area in 3 easy Steps
Calculating the area of a rectangle is a simple procedure just as a piece of cake. As you know, the area of a rectangle is the product of the rectangle's width with the length. Thus you can surely calculate the area of a rectangle in three easy steps.
The rectangle consists of 4 sides that are not equal in length. However, the opposite sides are equal in length to each other. In a rectangular shape, its long side is named as the length, whereas the shorter side is known as the width.
Therefore, to calculate the area of a rectangle, we can write its formula as
A = l x w
Although to calculate it in 3 easy steps, all we have to do is:
- First of all, identify the similar and opposite sides of the rectangle. Then take one value from the length's side and one from the width's side.
- Write them in the area of a rectangle formula. For instance, if we have 6cm for length and 4 cm as the width of the rectangle, we would write them as 6x4.
- Lastly, multiply both the values with each other, or you can also use arithmetic tables for having the product of both values. After multiplication, the value you get, i.e., 24, is the area of the rectangle.
Cross product and rectangle area are very useful and important concepts that help a lot in education or other walks of life. Students usually consider these to be very difficult to understand, but it's not difficult as with this, you see calculating the area of the rectangle and cross product of two vectors could be done in just 3 easy steps.