The vector product of vectors A⃗ and B⃗ has magnitude 12.0 m2 and is in the +z-direction. Vector A⃗ has magnitude 4.0 m and is in the −x-direction. Vector B⃗ has no x-component. Part A: What is the magnitude of vector B⃗ ? (I solved this question the answer is 3 and it's correct)Part B: What is the direction angle θ of vector B⃗ measured from the +y-direction to the +z-direction? (This is the part that I didn't get it correct)

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:

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).

show the wavelengths of a wave. show the crests of a wave.

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.