If $\overrightarrow { \mathbf { A } } = 7 \tilde { \mathbf { i } } - 6 \hat { \mathbf { j } } + 5 \hat { \mathbf { k } }$ , $| \overrightarrow { \mathbf { B } } | = 7$ ,and the angle between $\overrightarrow { \mathrm { A } }$ and $\vec { B }$ (when the two are drawn starting from the same point)is 60$\degree$,what is the scalar product of these two vectors?
A)-13
B)+13
C)+37
D)-37
E)73

Question

Quizplus · Accepted Answer

The scalar product (dot product) of two vectors $\overrightarrow { \mathbf { A } }$ and $\overrightarrow { \mathbf { B } }$ is given by $|\overrightarrow { \mathbf { A } }| |\overrightarrow { \mathbf { B } }| \cos(\theta)$. Here, $|\overrightarrow { \mathbf { A } }| = \sqrt{7^2 + (-6)^2 + 5^2} = \sqrt{110}$, $|\overrightarrow { \mathbf { B } }| = 7$, and $\theta = 60^\circ$. Thus, the dot product is $\sqrt{110} \times 7 \times \cos(60^\circ) = \sqrt{110} \times 7 \times \frac{1}{2} = 37$.

If A→=7i~−6j^+5k^\overrightarrow { \mathbf { A } } = 7 \tilde { \mathbf { i } } - 6 \hat { \mathbf { j } } + 5 \hat { \mathbf { k } }A=7i~−6j^​+5k^

If $\overrightarrow { \mathbf { A } } = 7 \tilde { \mathbf { i } } - 6 \hat { \mathbf { j } } + 5 \hat { \mathbf { k } }$