S6.12.3.17 Find the angle between the vectors

In summary, finding the angle between vectors is important for various scientific and mathematical applications. To find the angle, one can use the dot product or cross product formula, which depend on the vectors' magnitudes and orientation. The angle between vectors is always positive and can range from 0 to 180 degrees. Another method for finding the angle is using the cross product formula, which is useful for 3-dimensional vectors.
  • #1
karush
Gold Member
MHB
3,269
5
$\tiny{s6.12.3.17}\\$
$\textsf{ Find the angle between the vectors $a$ and $b$}\\$
\begin{align}
\displaystyle
a&=\langle 3,-1,5\rangle &b&=\langle -2,4,3\rangle\\
\\
\cos\left({\theta}\right)&=\frac{(3\cdot -2)+(-1\cdot4)+(5\cdot3)}
{|\sqrt{35}|\cdot|\sqrt{29}|}\\
&\approx 0.1569 \\
\arccos(0.1569)&\approx80.97^o\approx81^o
\end{align}
tried W|A but dot product ?
 
Physics news on Phys.org
  • #2
This looks correct. What's the problem exactly?
 
  • #3
What about the dot product are you referring to?

The working, at least up to the expression for cosine of theta, is correct.
 

Related to S6.12.3.17 Find the angle between the vectors

1. What is the purpose of finding the angle between vectors?

Finding the angle between vectors is important in many scientific and mathematical applications, such as calculating forces, determining the direction of motion, and solving trigonometric equations.

2. How do you find the angle between two vectors?

To find the angle between two vectors, you can use the dot product formula: Angle = cos^-1((a * b) / (|a| * |b|)), where a and b are the two vectors and |a| and |b| are their magnitudes.

3. Can the angle between vectors be negative?

No, the angle between vectors is always positive. However, the direction of the angle can be clockwise or counterclockwise, depending on the orientation of the vectors.

4. What is the range of possible values for the angle between vectors?

The angle between vectors can range from 0 degrees (when the vectors are parallel) to 180 degrees (when the vectors are antiparallel).

5. Are there any other methods for finding the angle between vectors?

Yes, you can also use the cross product formula: Angle = sin^-1(|a x b| / (|a| * |b|)), where a and b are the two vectors and |a| and |b| are their magnitudes. This method is useful when working with 3-dimensional vectors.

Similar threads

MHB T12.3.11 Find the angle between vectors
    • Calculus
Replies
2
Views
1K
MHB S4.13.t.71 angles of triangle PQR
    • Calculus
Replies
5
Views
3K
MHB S4.854.13.5.47 Find symmetric equations, angle between the planes
    • Calculus
Replies
4
Views
1K
MHB 231.12.3.19 angle between vectors
    • Calculus
Replies
3
Views
2K
MHB S6.12.25 find v in component form
    • Calculus
Replies
2
Views
1K
MHB 243.12.5.21 acute angle btw vectors
    • Calculus
Replies
2
Views
1K
MHB S6.793.12.4.33 Find the volume of the parallelepiped
    • Calculus
Replies
3
Views
1K
MHB 231.12.3.63 Determine the smallest distance between point and line
    • Calculus
Replies
1
Views
1K
MHB S4.13.5.41 relation of 2 planes
    • Calculus
Replies
4
Views
2K
MHB Angle b/w Velocity $\&$ Acceleration Vectors at $t=0$
    • Calculus
Replies
4
Views
4K

Hot Threads

Recent Insights

Back
Top