find the magnitude of vectors
A=?+4j+4k
B=?+2j+3K
if the angle them 15 deegre
a.) by scalar product
b.) by vector product
Are the two ? symbols the same numerical i component, or are they different? You have one equation in each case and can only have one unknown.
If the ? components are x, the scalar product is
A*B = x^2 + 8 + 12 = x^2 + 20
and it also equals
|A||B|cos15 = sqrt(x^2+16+16)*sqrt(x^2+4+9)cos15
In principle, you could now solve for x^2, but it would be messy.
x^2 + 20 = sqrt[(x^2+32)(x^2+13)]*0.9659
same i
To find the magnitude of vectors A and B using scalar product and vector product, we'll follow these steps:
a.) Scalar product:
The scalar product (also known as dot product) of two vectors A and B is given by the formula:
A · B = |A| |B| cos(θ)
where |A| and |B| are the magnitudes of vectors A and B respectively, and θ is the angle between the two vectors.
Given that the angle between vectors A and B is 15 degrees, we can substitute the known values into the formula to find the magnitude of vector A:
|A| = √(A · A)
= √(|A|^2)
= √((?^2) + (4^2) + (4^2))
= √(?^2 + 16 + 16)
= √(?^2 + 32)
Similarly, we can find the magnitude of vector B:
|B| = √(B · B)
= √(|B|^2)
= √((?^2) + (2^2) + (3^2))
= √(?^2 + 4 + 9)
= √(?^2 + 13)
b.) Vector product:
The vector product (also known as cross product) of two vectors A and B is given by the formula:
A × B = |A| |B| sin(θ) n
where |A| and |B| are the magnitudes of vectors A and B respectively, θ is the angle between the two vectors, and n is the unit vector perpendicular to the plane containing A and B in accordance with the right-hand rule.
The magnitude of vector A × B is given by:
|A × B| = |A| |B| sin(θ)
Again, using the known angle between vectors A and B as 15 degrees, we can substitute the known values into the formula to find the magnitude of vector A × B:
|A × B| = |A| |B| sin(θ)
= |A| |B| sin(15)
= √(?^2 + 32) * √(?^2 + 13) * sin(15)
Please note that we're unable to provide the exact numerical values of |A| and |B| as the first components of vectors A and B are missing. However, you can substitute the specific values you have for ? into the equations we provided to calculate the magnitude of the vectors using the scalar and vector products.