Question

Vector u has its initial point at (-7, 2) and its terminal point at (11, 5). Vector v has a direction opposite that of vector u, and its magnitude is three times the magnitude of u. What is the component form of vector v?
A. $v= \ \textless \ -54, 63\ \textgreater$
B. $v= \ \textless \ -162, -63\ \textgreater$
C.$v= \ \textless \ -54, 21\ \textgreater$
D. $v= \ \textless \ -162, 21\ \textgreater$

Answer 1

Here,

the initial point of vector u(x1,y1)=(-7,2)

the final point of vector u (x2,y2)=(11,5)

so the component of vector u(x,y)=(x2,y2)-(x1,y1)

=(11+7,5-2)=(18,3)

according to the question, the magnitude of vector is thrice the magnitute of vector u and is opposite ot the ditecrion of vector u.

so the component of vector v is -3(x,y)

=-3(18,3)=(-54,-9)