# Solving Vector Problems

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The Greek letters $\lambda$ and $\mu$ are often used as constants in vector equations, so why not get into the habit of using them for yourself?

(moderate) A car moves 150.0 m at a 63° "north of east" (this simply means 63° from the x-axis).

Then we may be informed that a vector is "simply" a quantity that has both magnitude and direction (unlike a scalar which only has magnitude).

Diagrams It is helpful to separate out some of these ideas about vectors in order to make sense of things.

Remember, $\mathbf.\mathbf=|a|^2$, and if two vectors are perpendicular, their scalar product is $0$.

Magnitude and direction Some vector problems involve a vector function which tells you how an object's position changes in time, for example.We are very used to expressing lines using cartesian geometry in the form $y=mx c$ and other variants.The vector equation of a line is no more complicated really, it's just a case of getting used to it.This short article aims to highlight some of the powerful techniques that can be used to solve problems involving vectors, and to encourage you to have a go at such problems to become more familiar with vector properties and applications. When we first meet them, it's often in the context of transformations - a translation can be expressed as a vector telling us how far something is translated to the right (or left) and up (or down).Confusion can strike when we come across vectors being used to indicate absolute position relative to an origin as well as showing a direction.Scalar products Scalar products are immensely useful!Sometimes if you're at a loss to know what to do with vectors and vector equations, it's worth just taking the scalar product of the whole equation with one of your vectors and seeing what you end up with.Vector questions can often be about geometrical shapes like trapezia, rhombuses or parallelograms.If two vectors are parallel, it can be really useful to express one in terms of the other - if $\mathbf$ and $\mathbf$ are parallel, try writing $\mathbf=k\mathbf$ for some constant $k$.Consider the point on the tire that was originally touching the ground.How far has it displaced from its starting position? (moderate) A student carries a lump of clay from the first floor (ground level) door of a skyscraper (on Grant Street) to the elevator, 24 m away. Finally, she exits the elevator and carries the clay 12 m back toward Grant Street.

• ###### Solving Problems with Vectors nrich.

Given a vector problem, a quick sketch can help you to see what's going on, and the act of transferring the problem from the written word to a diagram can often give you some insight that will help you to find a solution. Start by solving vector problems in two dimensions - it's easier to draw the diagrams - and then move on to three dimensions.…

• ###### Calculus II - Arc Length with Vector Functions Practice Problems

Here is a set of practice problems to accompany the Arc Length with Vector Functions section of the 3-Dimensional Space chapter of the notes for Paul Dawkins Calculus II course at Lamar University.…

• ###### Matrices, vectors, and solving simultaneous equation problems.

In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems.…

• ###### Vector Geometry solutions, examples, videos - Online Math Learning

Lessons on Vectors vectors in geometrical shapes, Solving Vector Problems, Vector Magnitude, Vector Addition, Vector Subtraction, Vector Multiplication, examples and step by step solutions, algebraic vectors, parallel vectors, How to solve vector geometry problems, Geometric Vectors with Application Problems…

• ###### Vector Resolution & Components - Practice - Physics

Resolve the vectors into their components along the x and y axes. Watch the signs. Then add the components along each axis to get the components of the resultant. Use these to get the magnitude and direction of the resultant. Problems with a lot of components are easier to work on when the values are written in table form like this…

• ###### Solving a System of Differential Equation by Finding Eigenvalues and.

Solving a System of Differential Equation by Finding Eigenvalues and Eigenvectors. one may write the solution as a single vector \ \mathbf{x}t=\begin{bmatrix}.…

• ###### Vector Worksheet - wou.edu

A Use vector addition to diagram the two vectors and calculate the resultant vector. B What is the direction of the jet’s velocity vector measured east of north? The rst step in solving any physics problem is to draw a diagram including all of the relevant information. So lets do that…