Direction cosines - vector, Mathematics

Assignment Help:

Direction Cosines

This application of the dot product needs that we be in three dimensional (3D) space not like all the other applications we have looked at to this point. 

Let us begin with a vector, a in three dimensional (3D) space.  This vector will make angles along with the x-axis (α), the y-axis (β), and the z-axis (γ).  These angles are known as direction angles and the cosines of these angles are known as direction cosines.

Here is a diagram of a vector and the direction angles.

1577_Direction Cosines - Vector.png

The formulas for the direction cosines are as follow:

cos α = a• i / ||a|| = a1 / ||a||

cos β = a • j / ||a|| = a2 / ||a||

cos γ = a • k / ||a|| = a3 / ||a||

where i, j, and k are the standard basis vectors.


Related Discussions:- Direction cosines - vector

How much area will it irrigate in 30 minutes , Water in a canal 30 dm wide ...

Water in a canal 30 dm wide and 12 dm deep is flowing with a velocity of 10 km/h. How much area will it irrigate in 30 minutes if 8 cm of standing water is required for irrigation?

Mass marketing, is mass marketing completely dead?

is mass marketing completely dead?

Parallelograns, Find x and y in each paarallelogram.

Find x and y in each paarallelogram.

Math, is this free for LIFE that means forever never ever going to pay

is this free for LIFE that means forever never ever going to pay

The perimeter square can be expressed as x + 4 estimate x, The perimeter of...

The perimeter of a square can be expressed as x + 4. If one side of the square is 24, what is the value of x? Since the perimeter of the square is x + 4, and a square has four

Find how much more space than the toy it will cover, A Solid toy in the for...

A Solid toy in the form of a hemisphere surmounted by the right circular cone of height  2cm  and  diameter  of  the  base  4  cm .If  a right  circular  cylinder circumscribes the

Holistic Marketing, Do you believe the holistic marketing concept is the mo...

Do you believe the holistic marketing concept is the most effective way to conduct marketing activities? Why? (Why not?)

Precalc, I dont understand arcsin and arccos and how to find the domain...h...

I dont understand arcsin and arccos and how to find the domain...help?

Draw tangent graph y = sec ( x ), G raph y = sec ( x ) Solution: As wi...

G raph y = sec ( x ) Solution: As with tangent we will have to avoid x's for which cosine is zero (recall that sec x =1/ cos x) Secant will not present at

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd