Given vectors a (2; -1; 4) and b (5; 3; x) at what value of x a to multiply b = 19?

From the condition, we are given two vectors a (2; -1; 4) and b (5; 3; x). We need to find at what value of the parameter x a * b = 19.

We’ll start by remembering what the product of vectors is.

So, to perform the multiplication of vectors, we must multiply the corresponding coordinates and add the products.

Let’s write the product of vectors and equate to 19.

2 * 5 – 1 * 3 + 4 * x = 19;

10 – 3 + 4x = 19;

4x = 19 – 10 + 3;

4x = 12;

x = 3.

At x = 3, the task condition is fulfilled.

Answer: x = 3.