Find all values of x such that (4, x, −6) and (2, x, x) are orthogonal. (enter your answers as a comma-separated list.)

The values of x that makes these vectors orthogonal are x = 2 and x = 4.

Step-by-step explanation:

Orthogonal vectors

Suppose we have two vectors:

Their dot product is:

They are ortogonal is their dot product is 0.

Solving quadratic equations:

To solve this problem, we are going to need tosolve a quadratic equation.

Given a second order polynomial expressed by the following equation:

.

This polynomial has roots such that , given by the following formulas:

Find all values of x such that (4, x, −6) and (2, x, x) are orthogonal.

These vectors are going to be orthogonal if:

This is a quadratic equation, in which . So

The values of x that makes these vectors orthogonal are x = 2 and x = 4.

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step-by-step explanation: