# Vector triangle question - please check me on this

• bcjochim07
In summary, the conversation discusses finding the type of triangle formed by given vertices using the dot product. The dot product is positive for all three angles, indicating that the triangle is acute. The student also asks for confirmation on their approach and notes that the assignment is due soon.
bcjochim07

## Homework Statement

The vertices of a triangle are given by points A: (2,-7,3) B: (-1,5,8), & C: (4,6,-1) Is this triangle acute, obtuse, or right?

## Homework Equations

dot product is positive : acute angle
dot product is negative : obtuse angle

## The Attempt at a Solution

My main question is: don't the vectors have to be arranged tail to tail before you can take the dot product to determine the angle between the vectors? That seems to be the way it is defined in my book.

The three vectors that make up the triangle are
AB: [-3,12,5]
AC: [2,13,-4]
BC: [5,1,-9]

AB$$\cdot$$AC= (-3)(2) + (12)(13) + (5)(-4)= 130 > 0, so angle BAC is acute.

AC$$\cdot$$BC = (2)(5) + (13)(1) + (-4)(-9) = 59 > 0, so angle ACB is acute
(This is the same as CA$$\cdot$$CB so they are tail to tail)

BC$$\cdot$$AB = (5)(-3) + (1)(12) + (-9)(5) = -48 < 0, but this is not the angle in the triangle, according to the picture I drew. Rather, this is the supplement, so the angle ABC is also acute.

Thus, the triangle is acute. Could somebody check my work please? Thanks.

nota bene: The ABAC, ACBC, & BCAB are supposed to be dot products.

Any ideas? This assignment is due tomorrow, and I'm pretty curious about whether I am doing this problem correctly or not.

## What is a vector triangle?

A vector triangle is a geometric representation of three vectors, typically shown graphically as three sides of a triangle. It is used to solve problems involving vector addition and subtraction.

## How do you solve a vector triangle question?

To solve a vector triangle question, you typically start by drawing a diagram of the given vectors. Then, you can use the triangle law or the parallelogram law to find the resultant vector. Finally, you can use trigonometry to find the magnitude and direction of the resultant vector.

## What is the triangle law of vector addition?

The triangle law of vector addition states that the resultant of adding two vectors can be found by placing the vectors head-to-tail and drawing a line from the tail of the first vector to the head of the second vector. The resultant vector is the line connecting the tail of the first vector to the head of the second vector.

## How do you use the parallelogram law to solve a vector triangle question?

The parallelogram law states that the resultant of adding two vectors can be found by constructing a parallelogram with the two vectors as adjacent sides. The diagonal of the parallelogram represents the resultant vector. You can then use trigonometry to find the magnitude and direction of the resultant vector.

## What are some common mistakes when solving vector triangle questions?

Common mistakes when solving vector triangle questions include forgetting to include the direction of the vectors, using incorrect units, and not using the correct trigonometric functions to find the magnitude and direction of the resultant vector. It is important to carefully label and draw the given vectors and to double-check your calculations for accuracy.

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