Find the magnitude of vectors
A=?+4j+4k
B=?+2j+3k
if angle between them 15 deegres
a) By scalar product
b) by vector product
PLEASE ANSWER MY ASSIGNMENT..WITH COMPLETE SOLUTION THANK U
a) To find the magnitude of vectors A and B using the scalar product, we can use the formula:
|A| = |B| * cos(theta)
where |A| represents the magnitude of vector A, |B| represents the magnitude of vector B, and theta represents the angle between the two vectors (15 degrees in this case).
First, we need to calculate the magnitude of vector B. Given B = ? + 2j + 3k, we can use the formula:
|B| = sqrt(Bx^2 + By^2 + Bz^2)
where Bx, By, and Bz represent the x, y, and z components of vector B, respectively.
In this case, Bx = ?, By = 2, and Bz = 3. Therefore,
|B| = sqrt((?^2) + 2^2 + 3^2)
Next, we can substitute the values into the magnitude formula:
|A| = |B| * cos(theta)
|A| = sqrt((?^2) + 2^2 + 3^2) * cos(15 degrees)
Finally, evaluate the expression to find the magnitude of vector A.
b) To find the magnitude of vectors A and B using the vector product, we can use the formula:
|A x B| = |A| * |B| * sin(theta)
where |A x B| represents the magnitude of the cross product of vectors A and B, |A| represents the magnitude of vector A, |B| represents the magnitude of vector B, and theta represents the angle between the two vectors (15 degrees in this case).
First, we need to calculate the magnitude of vector A. Given A = ? + 4j + 4k, we can use the formula:
|A| = sqrt(Ax^2 + Ay^2 + Az^2)
where Ax, Ay, and Az represent the x, y, and z components of vector A, respectively.
In this case, Ax = ?, Ay = 4, and Az = 4. Therefore,
|A| = sqrt((?^2) + 4^2 + 4^2)
Next, we can substitute the values into the magnitude formula:
|A x B| = |A| * |B| * sin(theta)
|A x B| = sqrt((?^2) + 4^2 + 4^2) * |B| * sin(15 degrees)
Finally, evaluate the expression to find the magnitude of the cross product of vectors A and B.