Vector a⃗ =aiˆ−bkˆ and vector b⃗ =−cjˆ+dkˆ. (a) in terms of the positive scalar quantities a, b, c, and d, what are a⃗ ⋅b⃗ and a⃗ ×b⃗ ? (b) if c=0, what is the magnitude of a⃗ ⋅b⃗ and what are the magnitude and direction of a⃗ ×b⃗ ? does your result for the direction for a⃗ ×b⃗ agree with the result you get if you sketch a⃗ and b⃗ in the xz-plane and apply the right-hand rule? the scalar product can be described as the magnitude of b⃗ times the component of a⃗ that is parallel to b⃗ . does this agree with your result? the magnitude of the vector product can be described as the magnitude of b⃗ times the component of a⃗ that is perpendicular to b⃗ . does this agree with your result?

Which property is illustrated by the following statement? if hxa rgi, then rgi hxa.

4+(2+x) can you me solve this problem

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).