When do vectors have the same magnitude

On separate pages, we discuss two different ways to multiply two vectors together: the dot product and the cross product. Recall such translation does not change a vector. The vector addition is the way forces and velocities combine. For example, if a car is travelling due north at 20 miles per hour and a child in the back seat behind the driver throws an object at 20 miles per hour toward his sibling who is sitting due east of him, then the velocity of the object relative to the ground!

The velocity vectors form a right triangle, where the total velocity is the hypotenuse. Therefore, the total speed of the object i. But, both sums are equal to the same diagonal of the parallelogram. You can explore the properties of vector addition with the following applet. This applet also shows the coordinates of the vectors, which you can read about in another page. The sum of two vectors. But orthogonal components was not asked for in the question.

One can represent it in other ways such as a derivative along a certain curve, popular in differential geometry. In 3D the direction part now is a 3D direction, which can be thought of as a unit vector, a point on the unit sphere, or the complex parts of a quaternion. However, when deciding how to represent a vector one also needs to consider what makes it easy to calculate with. So when inventing another representation you need to find the right formulas for how the components change under elementary operations.

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? So this is the square root of 25 which is able to five so their magnitude is the same. But notice that their components are not the axe important off a is five the X component of the is three.

The y component of a does not exist and the or is equal to zero, and the Y component of B is for so the answer is no. If one of the two components of a vector is not zero, can the magnitude of t… Can a vector have a component equal to zero and still have a nonzero magnitu… For each given vector, find another vector that has the same magnitude but a… Under what circumstances would a vector have components that are equal in ma… Fill in the blank.

Two vectors with the same magnitude and direction are … Problem What is wrong with the following expressions? View Full Video Already have an account?

Guilherme B. Problem 20 Easy Difficulty If two vectors have the same magnitude, do their components have to be the same? Answer No. View Answer. Topics Physics Basics. University Physics Volume 1 Chapter 2 Vectors. A vector quantity has two characteristics, a magnitude and a direction. When comparing two vector quantities of the same type, you have to compare both the magnitude and the direction. On this slide we show three examples in which two vectors are being compared.

Vectors are usually denoted on figures by an arrow. The length of the arrow indicates the magnitude and the tip of the arrow indicates the direction. The vector is labeled with an alphabetical letter with a line over the top to distinguish it from a scalar.