u=-1,3 and w= 2,-5. Find the component form of the vector.
3. 2u + 3w
A 0,1
B 5,-12
C 2,3
D 1,-2
E -3,8
F 4,-9
2u + 3w
= 2(-1,3) + 3(2,-5)
= (-2,6) + (6,-15)
= (4,-9)
or 4i - 9j in component form
To find the component form of the vector 2u + 3w, where u = (-1, 3) and w = (2, -5), we can perform vector addition by multiplying each component of u and w by their respective scalar values and then adding the corresponding components.
First, multiply u by 2:
2u = 2(-1, 3) = (-2, 6)
Next, multiply w by 3:
3w = 3(2, -5) = (6, -15)
Finally, add the corresponding components:
2u + 3w = (-2, 6) + (6, -15) = (-2 + 6, 6 - 15) = (4, -9)
Therefore, the component form of the vector 2u + 3w is F) 4, -9.
To find the component form of the vector 2u + 3w, we need to multiply each component of u and w by their respective scalars (2 and 3), and then add them together.
Given u = (-1, 3) and w = (2, -5):
Multiply u by 2: 2u = 2(-1, 3) = (-2, 6)
Multiply w by 3: 3w = 3(2, -5) = (6, -15)
Add the resulting vectors together: ( -2, 6 ) + ( 6, -15 ) = ( -2 + 6, 6 + (-15) ) = ( 4, -9 )
Therefore, the component form of the vector 2u + 3w is F) 4, -9.