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Answer:
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.