MATH SOLVE

4 months ago

Q:
# Let v = (1,-3) and w = (-2,6). Which of the following is true? Check all that apply. A.The x-component of v is -2. B. The y-component of w is 6. C. v+w = 36 D. w = -2v

Accepted Solution

A:

A) Vectors are usually given in the form (x , y), therefore the x-component of v is 1.

B) Similarly to point A), the y-component of w is 6

C) the magnitude of the vector v+w is given by:

√[(x₁ + x₂)² + (y₁ + y₂)²] = √[(1 + (-2))² + (-3 + 6)²] = √(1 + 9) =√10

D) Compute -2 · v = (-2·1 , -2·(-3)) = (-2 , 6) = w

Therefore options B) and D) are true.

B) Similarly to point A), the y-component of w is 6

C) the magnitude of the vector v+w is given by:

√[(x₁ + x₂)² + (y₁ + y₂)²] = √[(1 + (-2))² + (-3 + 6)²] = √(1 + 9) =√10

D) Compute -2 · v = (-2·1 , -2·(-3)) = (-2 , 6) = w

Therefore options B) and D) are true.