Janessa Benson

2022-09-06

I have two vectors:

$A:\{51.031,-102.062,51.031\}\text{}(|A|=125)$

$B:\{2,-4,-1\}\text{}(|B|=\sqrt{21}\approx 4.58)$

I am trying to find the amount of $\overrightarrow{A}$ in the $\overrightarrow{B}$ direction, so I used dot product with the coordinate method:

$({x}_{1}\times {x}_{2}+{y}_{1}\times {y}_{2}+{z}_{1}\times {z}_{2})$

$([2\times 51.031]+[-4\times -102.062]+[-1\times 51.031])=459.279$

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?

$A:\{51.031,-102.062,51.031\}\text{}(|A|=125)$

$B:\{2,-4,-1\}\text{}(|B|=\sqrt{21}\approx 4.58)$

I am trying to find the amount of $\overrightarrow{A}$ in the $\overrightarrow{B}$ direction, so I used dot product with the coordinate method:

$({x}_{1}\times {x}_{2}+{y}_{1}\times {y}_{2}+{z}_{1}\times {z}_{2})$

$([2\times 51.031]+[-4\times -102.062]+[-1\times 51.031])=459.279$

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?

Branson Perkins

Beginner2022-09-07Added 7 answers

The magnitude of A in B's direction (i.e. the magnitude of the projection of A onto B) is given by $\frac{A\cdot B}{|B|},$ not $A\cdot B.$

You can see that $A\cdot B$ 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 $|A|\mathrm{cos}\theta ,$, where $\theta $ is the angle between A and B. Recall that the dot product is given by $A\cdot B=|A||B|\mathrm{cos}\theta ,$ so $\frac{A\cdot B}{|B|}=|A|\mathrm{cos}\theta ,$, which is what we want

You can see that $A\cdot B$ 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 $|A|\mathrm{cos}\theta ,$, where $\theta $ is the angle between A and B. Recall that the dot product is given by $A\cdot B=|A||B|\mathrm{cos}\theta ,$ so $\frac{A\cdot B}{|B|}=|A|\mathrm{cos}\theta ,$, which is what we want

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix

$$\left[\begin{array}{cccc}1& 3& 0& -4\\ 2& 6& 0& -8\end{array}\right]$$ Find, correct to the nearest degree, the three angles of the triangle with the given vertices

A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)Whether f is a function from Z to R if

?

a) $f\left(n\right)=\pm n$.

b) $f\left(n\right)=\sqrt{{n}^{2}+1}$.

c) $f\left(n\right)=\frac{1}{{n}^{2}-4}$.How to write the expression ${6}^{\frac{3}{2}}$ in radical form?

How to evaluate $\mathrm{sin}\left(\frac{-5\pi}{4}\right)$?

What is the derivative of ${\mathrm{cot}}^{2}x$ ?

How to verify the identity: $\frac{\mathrm{cos}\left(x\right)-\mathrm{cos}\left(y\right)}{\mathrm{sin}\left(x\right)+\mathrm{sin}\left(y\right)}+\frac{\mathrm{sin}\left(x\right)-\mathrm{sin}\left(y\right)}{\mathrm{cos}\left(x\right)+\mathrm{cos}\left(y\right)}=0$?

Find $\mathrm{tan}\left(22.{5}^{\circ}\right)$ using the half-angle formula.

How to find the exact values of $\mathrm{cos}22.5\xb0$ using the half-angle formula?

How to express the complex number in trigonometric form: 5-5i?

The solution set of $\mathrm{tan}\theta =3\mathrm{cot}\theta $ is

How to find the angle between the vector and $x-$axis?

Find the probability of getting 5 Mondays in the month of february in a leap year.

How to find the inflection points for the given function $f\left(x\right)={x}^{3}-3{x}^{2}+6x$?

How do I find the value of sec(3pi/4)?