Question

Let be the vector with initial point d(8, 6) and terminal point e(–1, 5). Write it as a linear combination of the vectors i and j.

1) 9i + 14j
2) 4i + 7j
3) 11i - 9j
4) -i - j

Answer 1

To write the vector d(8, 6) - e(-1, 5) as a linear combination of the vectors i and j, subtract the x-coordinates and y-coordinates of the two points to find the coefficients for i and j, respectively. The resulting vector can be written as 9i + 1j.

Step-by-step explanation:

To write the vector d(8, 6) - e(-1, 5) as a linear combination of the vectors i and j, we need to find the coefficients a and b such that the vector can be expressed as a*i + b*j.

To find a and b, we can subtract the x-coordinates of the first and second points to find the coefficient for i, and subtract the y-coordinates to find the coefficient for j. The x-coordinate difference is 8 - (-1) = 9, and the y-coordinate difference is 6 - 5 = 1.

Therefore, the vector d(8, 6) - e(-1, 5) can be written as 9i + 1j, which is closest to option 2) 9i + 14j.