Video Transcript
If 𝐀 equals four, 𝑚; 𝐁 equals
three, six; and 𝐀 is perpendicular to 𝐁, then 𝑚 equals what.
Alright, so here, given vectors 𝐀
and 𝐁, we want to solve for this value 𝑚, which makes 𝐀 perpendicular to 𝐁. In general, if we have a vector 𝐕
one and it’s perpendicular to another vector 𝐕 two, then that means the dot product
of these two vectors is zero. We can apply this fact to our
scenario with vectors 𝐀 and 𝐁. Since they are perpendicular, 𝐀
dot 𝐁 equals zero. And therefore, four, 𝑚 dot three,
six equals zero.
We can begin carrying out this dot
product by multiplying together the corresponding components of these vectors. We get that four times three plus
𝑚 times six equals zero or 12 plus six 𝑚 equals zero. If we subtract 12 from both sides
of this equation, we have that six 𝑚 equals negative 12. And then dividing both sides by
six, we find that 𝑚 equals negative two. We can fill in our blank then, and
the sentence now reads if 𝐀 equals four, 𝑚; 𝐁 equals three, six; and 𝐀 is
perpendicular to 𝐁, then 𝑚 equals negative two.
