# Calc 3: Vector Addition Problem Solution Example

• mikky05v
In summary, the conversation is about a student struggling with a homework problem involving vectors and their lengths. They share their attempt at solving the problem and are unsure if their answer is correct due to multiple choice options being very close to their calculated answer. Another person reassures them that their answer is correct and reminds them that it is not necessary to calculate every answer down to the last decimal place.

#### mikky05v

I'm trying to do this homework problem but I keep getting an answer that is not given. Can someone tell me what I am doing wrong please. This is for University level calc 3.

## Homework Equations

A vector U=<x,y>
||U|| means the length of U = √(x^2 +y^2). vectors can also be written as U = ||U||(cosθi, sinθj)

## The Attempt at a Solution

so I start by naming the vectors.V is the direction the plane is now heading. V1 is the original direction of the plane. V2 is the direction of the wind.

V = V1 + V2

V1 = 600(cos148i+sin148j)
V2 = 80(cos45i+sin45j)

next I distributed, combined like terms and factored out i and j
V = (600cos148+80cos45)i + (600sin148+80cos45)j

I plugged that into my calculator and got
V = <-452.7i + 374.5j>

To find the speed I found the length of vector V
||V|| = sqrt[ (-452.7)2+374.52] = 587.5 km/hr

That isn't one of the options.. am i wrong?

587.5 versus 587.2 km/hr. Hmmm. That's a mighty big difference.

ya i realize it's extremely close but it is also multiple choice. being "close" to one of 5 possible answers doesn't exactly make me feel confident I am doing it right. Do you have anything helpful to add?

mikky05v said:
ya i realize it's extremely close but it is also multiple choice. being "close" to one of 5 possible answers doesn't exactly make me feel confident I am doing it right. Do you have anything helpful to add?

It's rare that you are going to calculate every answer down to the last decimal place.

Would you feel more confident of your approach if NONE of the choices came close to your answer?

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## 1. What is vector addition in Calc 3?

Vector addition in Calc 3 is the process of combining two or more vectors to find their resultant vector. This is done by adding the corresponding components of each vector and finding the magnitude and direction of the resultant vector.

## 2. How is vector addition different in Calc 3 compared to Calc 1 or 2?

In Calc 1 and 2, vector addition is done in two dimensions, while in Calc 3 it is done in three dimensions. This means that in Calc 3, vectors have three components (x, y, and z) instead of just two (x and y).

## 3. What is the process for adding two vectors in Calc 3?

The process for adding two vectors in Calc 3 involves finding the sum of their corresponding components, then using the Pythagorean theorem to find the magnitude of the resultant vector. The direction of the resultant vector can be found using trigonometric functions or by using the dot product.

## 4. Can vector addition be done with more than two vectors in Calc 3?

Yes, vector addition can be done with any number of vectors in Calc 3. The process is the same as adding two vectors, but it must be repeated for each additional vector. The resultant vector is the sum of all the individual vectors.

## 5. Why is vector addition important in Calc 3?

Vector addition is important in Calc 3 because it allows us to analyze and understand physical quantities, such as forces and velocities, in three-dimensional space. It is also an essential tool in many fields of science, including physics, engineering, and computer graphics.