Answer: The correct option are
(A) v and w are perpendicular.
(D) w = -4(-3,-1).
Step-by-step explanation: We are given two vectors 'v' and 'w' as follows:
[tex]v=(-2,6),\\\\w=(12,4).[/tex]
We are to select the correct statement about these two vectors.
We know that two vectors are perpendicular to each other if their dot product is zero.
We have
[tex]v.w=(-2,6).(12,4)=-2\times 12+6\times 4=-24+24=0.[/tex]
So, the two vectors are perpendicular.
Option (A) is correct.
Since the x-component of 'v' is -2, so option (B) is incorrect.
Since the product f 'v' and 'w' is 0, so it cannot equal to 48. Option (C) is also incorrect.
Now,
[tex]w=(12,4)=-4(-3,-1).[/tex]
So, option (D) is also correct.
Thus, the correct options are (A) and (D).
