Scalar product to find angle between two vectors

In summary, the angle between the two vectors given by a = 2.0 i + 6.0 j + 2.0 k and b = 4.0 i + 3.0 j + 6.0 k is 42.79 degrees, calculated using the definition of scalar product and the values of a and b.
  • #1
noeinstein
14
0
Use the definition of scalar product, a·b = ab cos , and the fact that a·b = axbx + ayby + azbz (see Problem 46) to calculate the angle between the two vectors given by a = 2.0 i + 6.0 j + 2.0 k and b = 4.0 i + 3.0 j + 6.0 k.

AdotB= 8i + 18j + 12k

A=sqrt(2^2 + 6^2 + 2^2)=6.63
B=sqrt(4^2 + 3^2 + 6^2)=7.81

AdotB=(6.63)(7.81)cosΘ

Θ=acos(38/51.78)

Θ=42.79=WRONG
 
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  • #2
Check your arithmetic.
 
  • #3
I went over it again and got the same answer.
 
  • #4
Then why do you think it's wrong?
 
  • #5
because the online assignment is giving me a big fat red X. lol
 
  • #6
Then I'll admit to making whatever mistake you've apparently made. :D
 
  • #7
Never mind. Got it. I switched the values of ay and by. Thanks.
 
  • #8
:d.. dah
 

1. What is a scalar product?

A scalar product, also known as dot product, is a mathematical operation that takes two vectors and produces a scalar quantity. It is calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them.

2. How do you find the scalar product?

To find the scalar product, you need to multiply the corresponding components of the two vectors and then sum up the products. For example, if the two vectors are A = (a1, a2, a3) and B = (b1, b2, b3), the scalar product can be calculated as A · B = (a1 * b1) + (a2 * b2) + (a3 * b3).

3. What is the significance of the scalar product?

The scalar product has multiple applications in physics, engineering, and mathematics. It is used to calculate work done, find the angle between two vectors, determine if two vectors are perpendicular, and in the projection of one vector onto another.

4. How can the scalar product be used to find the angle between two vectors?

The angle between two vectors can be found by using the formula: cos θ = (A · B) / (|A| * |B|), where θ is the angle between the two vectors and |A| and |B| represent the magnitudes of the vectors. By rearranging the formula, the angle can be calculated as θ = cos^-1[(A · B) / (|A| * |B|)].

5. Can the scalar product be negative?

Yes, the scalar product can be negative if the angle between the two vectors is greater than 90 degrees. This means that the two vectors are pointing in opposite directions, resulting in a negative scalar product. If the angle is less than 90 degrees, the scalar product will be positive.

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