Two Vectors $\overrightarrow { \mathrm { A } }$ And $\vec { B }$

Two vectors $\overrightarrow { \mathrm { A } }$ and $\vec { B }$ are given by $\overrightarrow { \mathbf { A } } = 4 \hat { \mathbf { i } } + 8 \hat { \mathbf { j } }$ and $\overrightarrow { \mathbf { B } } = 6 \hat { \mathbf { i } } - 2 \hat { \mathbf { j } }$ .The scalar product of $\overrightarrow { \mathrm { A } }$ and a third vector $\overrightarrow { \mathrm { C } }$ is -16.The scalar product of $\vec { B }$ and $\overrightarrow { \mathrm { C } }$ is +18.The z component of $\overrightarrow { \mathrm { C } }$ is 0.What is the magnitude of $\overrightarrow { \mathrm { C } }$ ?

A) 7.8
B) 6.4
C) 3.6
D) 5.0
E) 4.8

Correct Answer:

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