Video Transcript
Which of the following vectors is
not perpendicular to the line whose direction vector 𝐫 is six, negative five? Is it (A) 𝐫 is equal to negative
five, negative six? (B) 𝐫 is equal to five, six. (C) 𝐫 is equal to 10, 12. Or (D) 𝐫 is equal to 12, negative
10.
We recall that two vectors are
perpendicular if their scalar or dot product is equal to zero. To calculate the scalar product, we
find the sum of the product of the individual components. For option (A), we need to multiply
six by negative five and then add negative five multiplied by negative six. Multiplying a positive number by a
negative number gives a negative answer. And multiplying two negative
numbers together gives a positive answer. This leaves us with negative 30
plus 30. As this is equal to zero, the two
vectors are perpendicular. Option (A) is therefore not the
correct answer.
Repeating this process for option
(B), we have six multiplied by five plus negative five multiplied by six. This simplifies to 30 plus negative
30. Once again, this is equal to
zero. So option (B) is not correct. In option (C), we have six
multiplied by 10 plus negative five multiplied by 12. Six multiplied by 10 is equal to
60, and negative five multiplied by 12 is equal to negative 60. Option (C) is not the correct
answer as the scalar product equals zero.
In option (D), our calculation is
six multiplied by 12 plus negative five multiplied by negative 10. Six multiplied by 12 is 72, and
negative five multiplied by negative 10 is positive 50. This means that the scalar product
is equal to 122. This is not equal to zero. Option (D) is therefore the correct
answer. The vector 12, negative 10 is not
perpendicular to the line whose direction vector is six, negative five. This is because their scalar
product is not equal to zero.
