Video Transcript
Given that nine, one and negative
eight, 𝑚 are the direction vectors of two perpendicular straight lines, determine
the value of 𝑚.
In this question, we are given the
direction vectors of two straight lines, and we are told they are perpendicular to
one another. We recall that perpendicular lines
meet at 90 degrees. And if two perpendicular lines have
direction vectors 𝐝 sub one and 𝐝 sub two, then the dot or scalar product of 𝐝
sub one and 𝐝 sub two equals zero. In this question, the two direction
vectors are nine, one and negative eight, 𝑚. This means that the dot product of
these vectors must equal zero. And we can calculate the dot
product of any two vectors by finding the sum of the products of their corresponding
components.
This gives us nine multiplied by
negative eight plus one multiplied by 𝑚. Our equation simplifies to negative
72 plus 𝑚 is equal to zero. And adding 72 to both sides gives
us 𝑚 is equal to 72. If nine, one and negative eight, 𝑚
are the direction vectors of two perpendicular straight lines, then the value of 𝑚
is 72.
