Explain what is meant by perpendicular vectors and tail-to-tail method
Perpendicular vectors are two vectors that intersect at a right angle, or 90 degrees. When two vectors are perpendicular to each other, their dot product is zero. Geometrically, this means that the vectors do not share any common direction, and they are independent of each other.
Now, let me explain the tail-to-tail method for visualizing and determining the sum or resultant of perpendicular vectors.
The tail-to-tail method, also known as the parallelogram method, is a graphical technique used to find the vector sum or resultant of two perpendicular vectors. It is called tail-to-tail method because vectors are represented by arrows, and the tails of these arrows are placed together to form a parallelogram.
To apply the tail-to-tail method:
1. Draw the two vectors, starting from a common origin point. These vectors should be drawn with their tails at the same point.
2. Using a ruler, draw a line parallel to one of the vectors, starting from the tip of the other vector. This line completes the parallelogram.
3. Locate the vector sum or resultant by drawing a diagonal line from the common origin point to the opposite corner of the parallelogram. The diagonal line represents the sum or resultant of the two vectors.
4. Measure the length and determine the direction of the diagonal line using a protractor or angle measurement tool. The length of the diagonal line represents the magnitude of the resultant vector, while the direction represents its direction in space.
So, in summary, perpendicular vectors are those that meet at a right angle, and the tail-to-tail method is a graphical technique used to determine the sum or resultant of these vectors by constructing a parallelogram.