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2 years ago

For what values of b are the vectors [-6,b,2] and [b,b2,b] orthognal

Mathematics

1 answer:

DanielleElmas [232]2 years ago

4 0

Answer:

b = 2, 0, -2

Step-by-step explanation:

This is a multivariable calculus question and two vectors are orthogonal if and only if their dot product is zero. Since

[-6,b,2] . [b,b²,b] = -6b + b³ + 2b

= -4b + b³

=b (4+b²)

== b (2²+b²)

==b (b-2)(b+2)

The given vectors are orthogonal if b = −2,

b = 0,

b = 2

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