The angle between two force a and b vectors is 114o. The scalar projection of is –
13 N. Determine the magnitude of b.
Can the magnitude be a negative number?
will the answer to this question be a positive number?
no, the magnitude is not negative. The cosine of 114 is negative.
-.407
|a| |b| cos 114 = -13
need to know |a| to get |b|
No, the magnitude of a vector cannot be negative. Magnitude represents the quantity or size of a vector, and it is always a positive value or zero. However, the scalar projection of a vector can be negative if it is pointing in the opposite direction of the reference axis chosen.
To determine the magnitude of vector b, we can use the formula for the scalar projection of vector a onto vector b:
Scalar Projection of a onto b = |a| * cos(theta)
where |a| represents the magnitude of vector a, and theta represents the angle between vectors a and b.
In this case, the scalar projection of a is given as -13 N, and theta is given as 114 degrees.
Therefore, we can rearrange the formula to solve for the magnitude of vector b:
|b| = Scalar Projection of a onto b / cos(theta)
|b| = (-13 N) / cos(114 degrees)
Calculating this expression, we find the magnitude of vector b.