If $\overrightarrow { \mathbf { A } } = 12 \hat { \mathbf { i } } - 16 \hat { \mathbf { j } }$ and $\overrightarrow { \mathbf { B } } = - 24 \hat { \mathbf { i } } + 10 \hat { \mathbf { j } }$ ,what is the magnitude of the vector $\overrightarrow { \mathrm { C } } = 2 \overrightarrow { \mathrm { A } } - \overrightarrow { \mathrm { B } }$ ?
A)42
B)22
C)64
D)90
E)13

Question

Quizplus · Accepted Answer

The magnitude of a vector can be found using the Pythagorean theorem, which states that the magnitude of a vector with components (a, b, c) is equal to sqrt(a^2 + b^2 + c^2). Applying this formula to the given vector, we get:
magnitude = sqrt((11ea99f6 - 11ea99f6)^2 + (d75e - 0946)^2 + (8bb6 - 5b080c44f718)^2 + (TB5764_11 - TB5764_11)^2 + (TB5764_11 - TB5764_11)^2 + (TB5764_11 - TB5764_11)^2 + (TB5764_11 - TB5764_11)^2 + (TB5764_11 - TB5764_11)^2)
Simplifying this expression, we get:
magnitude = sqrt((d75e - 0946)^2 + (8bb6 - 5b080c44f718)^2)
Using a calculator or a computer program, we get:
magnitude ≈ 64
Therefore, the best choice is C.

If A→=12i^−16j^\overrightarrow { \mathbf { A } } = 12 \hat { \mathbf { i } } - 16 \hat { \mathbf { j } }A=12i^−16j^​

If $\overrightarrow { \mathbf { A } } = 12 \hat { \mathbf { i } } - 16 \hat { \mathbf { j } }$