### Video Transcript

If vector π is equal to β, β plus
two and vector π is equal to three β, four β minus one, then one of the values of β
that makes vector π parallel to vector π is what. Is it (A) five, (B) seven, (C)
negative five, or (D) negative seven?

We recall that two vectors π and π
are parallel if vector π is equal to some nonzero constant π multiplied by vector
π. One way of answering the question
would be to substitute all four of the values in for β and see which one satisfies
the property. Alternatively, we can solve the
question using an algebraic method. For the two vectors to be parallel,
the vector β, β plus two must be equal to π multiplied by three β, four β minus
one. We can multiply any vector by a
scalar by multiplying each of the individual components by that scalar. The right-hand side simplifies to
three πβ, π multiplied by four β minus one.

This equation will now be true when
the individual components are equal. This means that β must be equal to
three πβ. As none of the options given are
zero, we are looking for a solution that is not equal to zero. This means that we can divide
through by β, giving us three π is equal to one. Dividing both sides of this
equation by three gives us a value of π equal to one-third. If we now consider the
π¦-components of our vector, we see that β plus two is equal to π multiplied by
four β minus one. Substituting π equals one-third,
the right-hand side becomes one-third multiplied by four β minus one.

There are many ways to solve this
equation. One way is to multiply both sides
by three. The left-hand side becomes three β
plus six. And this is equal to four β minus
one. We can then add one and subtract
three β from both sides, giving us six plus one is equal to four β minus three
β. Simplifying this, we get a value of
β equal to seven. This means that the correct answer
is (B). One of the values of β that makes
π parallel to π is seven.