# Math Help - I am looking for help with the following

1. ## I am looking for help with the following

The book states

Three Vectors

U= Uxi + 3j+2k
V= -3i + Vyj+3k
W= -2i + 4j+Wzk

are mutally perpendicular Use dot product to solve for the componets
Ux,Vy & Wz

I do not know how to begin and am pretty confused the answer are

Ux=2.875
Vj= .857
Wz=-3.143

Can anyone help??

2. Originally Posted by jaycas21
The book states

Three Vectors

U= Uxi + 3j+2k
V= -3i + Vyj+3k
W= -2i + 4j+Wzk

are mutally perpendicular Use dot product to solve for the componets
Ux,Vy & Wz

I do not know how to begin and am pretty confused the answer are

Ux=2.875
Vj= .857
Wz=-3.143

Can anyone help??
You have three unknowns Ux, Vy and Wz. You are told that they are
mutually perpendicular, and you are to use the dot product.

The dot product of perpendicular vectors is zero, so you have:

U.V=0,
U.W=0,
V.W=0.

Form these dot products and you will have three linear simultaneous
equations which you then need to solve.

Dot product of two vectors: $x_1i+x_2j+x_3k$ and $y_1i+y_2j+y_3k$ is:

$x_1y_1+x_2y_2+x_3y_3$,

where $i$, $j$ and $k$ are the unit vectors along a set of perpendicular axes.

RonL

3. I am still not getting the answers in the book

4. Originally Posted by jaycas21
The book states

Three Vectors

U= Uxi + 3j+2k
V= -3i + Vyj+3k
W= -2i + 4j+Wzk

are mutally perpendicular Use dot product to solve for the componets
Ux,Vy & Wz

I do not know how to begin and am pretty confused the answer are

Ux=2.875
Vj= .857
Wz=-3.143

Can anyone help??
If two vectors are perpendicular, then their dot product is zero.

Since the 3 given vectors are mutually perpendicular, then,
U dot V = 0
U dot W = 0
V dot W = 0

U dot V = (Ux)(-3) +3(Vy) +2(3) = 0
-3Ux +3Vy +6 = 0
-Ux +Vy +2 = 0 --------------(1)

U dot W = (Ux)(-2) +3(4) +2(Wz) = 0
-2Ux +12 +2Wz = 0
-Ux +6 +Wz = 0 -------------(2)

V dot W = -3(-2) +(Vy)(4) +3(Wz) = 0
6 +4Vy +3Wz = 0 --------(3)

3 equations, 3 unknowns, solvable.

(2) minus (1),
6 +Wz -Vy -2 = 0
Wz = Vy -6 +2
Wz = Vy -4 --------------(i)

Substitute that into (3),
6 +4Vy +3(Vy -4) = 0
6 +4Vy +3Vy -12 = 0
7Vy -6 = 0
7Vy = 6
Vy = 6/7 = 0.857 ----------answer.

Substitute that into (i),
Wz = 0.857 -4 = -3.143 ---------answer.

Substitute the 0.857 for Vy into (1),
-Ux +Vy +2 = 0 -----(1)
-Ux +0.857 +2 = 0
-Ux +2.857 = 0

------------------------
Zeez, late again.

5. Originally Posted by jaycas21
The book states
U= Uxi + 3j+2k
V= -3i + Vyj+3k
W= -2i + 4j+Wzk

Ux=2.875
Vj= .857
Wz=-3.143

Can anyone help??
U.V=-3Ux+3Vy+6=0 .......equation1
U.W=-2Ux+12+2Wz=0 ....equation2
V.W=6+4Vy+3Wz=0 .......equation3

This system has the solution that your book gives (as can be checked
by substituting its values into the equations.

RonL