Finding cross product of two vectors a,b

In summary, the conversation discussed finding the scalar and vector products of two vectors with given magnitudes and a 27° difference in direction. The scalar product was found using the formula a*b=abcos(theta) and the vector product was found using the right-hand rule, resulting in the answer of 17(7.4)(sin(27)) for the magnitude of the vector product. The geometric reasoning behind this solution was not fully understood.
  • #1
mmattson07
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0

Homework Statement


A vector of magnitude 17 units and another vector of magnitude 7.4 units differ in directions by 27°. Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product ×.

Homework Equations



Right-hand rule, a*b=abcos(theta), A x B= absin(theta)

The Attempt at a Solution


Dot product => a*b= (17)(7.4)(cos(27))= 112.089

Just not quite sure on how to do the cross product. The right hand rule gives me a vector pointing straight up the z axis when sweeping into b but not sure what values to plug into absin(theta) Thanks.
 
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  • #2
Hm. It seems the answer is just 17(7.4)(sin(27). Not sure geometrically why this is the case though.
 

Related to Finding cross product of two vectors a,b

1. What is the cross product of two vectors?

The cross product of two vectors, denoted as a × b, is a vector that is perpendicular to both a and b. It is defined as the product of the magnitudes of the two vectors and the sine of the angle between them.

2. How do you calculate the cross product of two vectors?

The cross product can be calculated by finding the determinant of a 3x3 matrix with the first row being the unit vectors i, j, and k, the second row being the components of vector a, and the third row being the components of vector b.

3. What is the geometric interpretation of the cross product?

The cross product has a geometric interpretation as the area of the parallelogram formed by the two vectors a and b. The direction of the cross product is perpendicular to this plane.

4. How is the cross product related to the dot product?

The cross product and dot product are two different ways of multiplying vectors. The dot product results in a scalar quantity while the cross product results in a vector. The magnitude of the cross product can be calculated using the dot product and sine of the angle between the vectors.

5. In what applications is the cross product used?

The cross product is commonly used in physics, engineering, and computer graphics. It is used for calculating torque and angular momentum in physics, finding the direction of torque in engineering, and determining the orientation of objects in 3D graphics.

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