I have two vectors: A:{51.031,−102.062,51.031} (|A|=125) B:{2,−4,−1} (|B|=sqrt(21)~~ 4.58) I am trying to find the amount of vec(A) in the vec(B) direction

Janessa Benson 2022-09-06 Answered
I have two vectors:
A : { 51.031 , 102.062 , 51.031 }   ( | A | = 125 )
B : { 2 , 4 , 1 }   ( | B | = 21 4.58 )
I am trying to find the amount of A in the B direction, so I used dot product with the coordinate method:
( x 1 × x 2 + y 1 × y 2 + z 1 × z 2 )
( [ 2 × 51.031 ] + [ 4 × 102.062 ] + [ 1 × 51.031 ] ) = 459.279
If the dot product is supposed to find the magnitude of a vector that is pointing in the direction of another vector, how do I get a result that's more than 3 times the length of the longest vector?
What am I doing wrong?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Branson Perkins
Answered 2022-09-07 Author has 7 answers
The magnitude of A in B's direction (i.e. the magnitude of the projection of A onto B) is given by A B | B | , not A B .
You can see that A B is wrong by units, too, since it has the units of A times B, rather than A. If we situate B on the x-axis, we want | A | cos θ ,, where θ is the angle between A and B. Recall that the dot product is given by A B = | A | | B | cos θ , so A B | B | = | A | cos θ ,, which is what we want
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-05-29
Which of the following expressions are meaningful? Which are meaningless? Explain.
a) (ab)c
(ab)c has ? because it is the dot product of ?.
b) (ab)c
(ab)c has ? because it is a scalar multiple of ?.
c) |a|(bc)
|a|(bc) has ? because it is the product of ?.
d) a(b+c)
a(b+c) has ? because it is the dot product of ?.
e) ab+c
ab+c has ? because it is the sum of ?.
f) |a|(b+c)
|a|(b+c) has ? because it is the dot product of ?.
asked 2021-02-11
Let F be a fixed 3x2 matrix, and let H be the set of all matrices A in M2×4 with the property that FA = 0 (the zero matrix in M3×4). Determine if H is a subspace of M2×4
asked 2021-05-29

Find the vector and parametric equations for the line segment connecting P to Q.
P(0, - 1, 1), Q(1/2, 1/3, 1/4)

asked 2021-05-17
Find the scalar and vector projections of b onto a.
a=(4,7,4),b=(3,1,1)
asked 2021-12-16
Vector Dot Product Learning Goal: To understand the rules for computing dot products. Let vectors A=(2,1,4),B=(3,0,1)
Angle between the vectors A and B What is the angle θAB between A and B? Express your answer numerically to three significant figures in radians. θAB= radians
asked 2021-02-02
Construct a vector that is orthogonal to 24i + 7j. You must have BOTH solutions.
asked 2022-09-19
Trying to prove:
Show that there are no vectors u and v such that u = 1, v = 2, and u v = 3
Don't know where to go from here:
u = 2 u 2 = 4 u u = 1
v = 1 v 2 = 1 v v = 4
Not sure if this is the right direction to take, but we have:
u v = v v u u = 3 = ( v + u ) ( v u )

New questions