(b) find real numbers a and b such that (a, 2, b. is orthogonal to both (−1, −2, 3) and (3, −2, 6).

Two vectors are orthogonal if their scalar product is zero. The scalar product of two vectors is computed as follows:

In other words, you multiply each component of the first vector with the correspondant component of the second vector, and then you sum all these products.

So, we need to compute the two scalar products, and set them to zero:

We can rewrite the two requests in this linear system:

From the first equation we can deduce , which substituted in the second gives

If we substitute this value for b in the first equation we have

where r the answers

step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!