Answer :
Answer:
θ=180°
Explanation:
The problem says that the vector product of A and B is in the +z-direction, and that the vector A is in the -x-direction. Since vector B has no x-component, and is perpendicular to the z-axis (as A and B are both perpendicular to their vector product), vector B has to be in the y-axis.
Using the right hand rule for vector product, we can test the two possible cases:
- If vector B is in the +y-axis, the product AxB should be in the -z-axis. Since it is in the +z-axis, this is not correct.
- If vector B is in the -y-axis, the product AxB should be in the +z-axis. This is the correct option.
Now, the problem says that the angle θ is measured from the +y-direction to the +z-direction. This means that the -y-direction has an angle of 180° (half turn).
The vector combination of two vectors is orthogonal to the two vectors; in this case, its product is now in the +z-direction, so vectors A and B are in the x-y plane.
- Now, since vector A is in the -x -direction but vector B has no x-component, vector B is also parallel towards the x-axis.
- The product has always been in the +z-direction, vector A has been in the -x -direction, and vector B has been parallel to both the product and vector A.
- As per the right-hand thumb rule vector B would be in either the +y or -y-direction. B would now be in the -y-direction.
- Since AB is the vector product of [tex](-x)\times (-y) =(+z)[/tex]. Since vector B is in the -y-direction, [tex]\angle \theta[/tex] [tex]= 180^{\circ}[/tex].
Therefore, the final answer is "[tex]180^{\circ}[/tex]".
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