PsychonautQQ said:Homework Statement
A constant force of 1i - 5j -8k moves (1,-4,2) (-3,2,-1), what is the work done on the particle?Homework Equations
Avector*Bvector=ABsinθ
?? I think?
The Attempt at a Solution
I really am quite lost... but I found the coordinates for the position vector...
(-3-1)i + (2--4j) + (-1-2)k and the magnitude of the position vector is 7.81
so the unit vector is -.512i + .768j -.384k... am I on the right track here?
PsychonautQQ said:so the force is 1i - 5j -8k and the displacement is -4i +6j -3k? so dot product would be -4 -30 - 24 = -58?
PsychonautQQ said:How do I find the angel between these vectors?
The dot product, also known as the scalar product, is a mathematical operation that takes two vectors and produces a scalar quantity. It is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them.
The dot product can be calculated by multiplying the corresponding components of the two vectors and then summing the products. It can also be calculated using the magnitudes of the two vectors and the angle between them.
The dot product has several important applications in mathematics and physics. It can be used to find the angle between two vectors, determine if two vectors are orthogonal, and calculate the work done by a force on an object.
Yes, the dot product can be negative. This occurs when the angle between the two vectors is greater than 90 degrees, resulting in a negative cosine value. A positive dot product indicates that the two vectors are pointing in the same general direction, while a negative dot product indicates they are pointing in opposite directions.
The dot product is used in the formula for vector projection, which is a method for finding the component of one vector in the direction of another vector. It is also used to calculate the magnitude of a vector projection.