Answer to Question #86504 in Mechanics | Relativity for Joshua

Question

2. ___ is a vector as a way of determining the magnitude and direction in its coordinate of x and y axis
a.Component of a vector in terms of identity vector
b.Component of a vector in terms of unit vector
c.Component of a vector in terms of free vector
dComponent of a vector in terms of block vector

3. If a=10, b=13 and the angle between a and b is 59.5 degree, what is the scalar product of a and b
a.65.98
b.65.9
c.65.95
d.65.93

Answer 1

Comments on question "2":

In order to define both magnitude and direction of vector components along the axes (here we consider the x- and y- axes of the Cartesian coordinate system), unit base vectors are commonly used. These are the vectors which have length (magnitude) equal to 1 and point along the corresponding axis direction. Thus, one should choose "b" as an answer.

Comments on question "3":

The scalar (dot) product of two vectors should be calculated in the way as follows:

$$\vec{a} \cdot \vec{b} = ab \cos{\theta},$$

where theta is the angle between the vectors. Substituting the numerical values, we obtain:

$$\vec{a} \cdot \vec{b} = 10 \cdot 13 \cdot \cos{59.5^∘} \approx 65.98$$

Thus, one should choose "a" as an answer.

Answer: 2.b ; 3.a