向量术语实践问题Online

Which of the following is a vector quantity?

The displacement from New York to London
The color of a shoe
The number of books on a shelf
An array with the number of books reads by each student in a class
The speed of an airplane

Which of the following vectors in the regular hexagon below has the same magnitude as $\vec{AB}$ but opposite direction?

Details and assumptions:

O is the intersection point of the three diagonal lines.

\vec{CO}

\vec{AF}

\vec{ED}

\vec{FO}

If $\vec{a}=\vec{b},$ which of the following is/are true?

I. $\vec{a}$ and $\vec{b}$ are parallel.
II. $\vec{a}$ and $\vec{b}$ are equal in magnitude.
III. The initial points of $\vec{a}$ and $\vec{b}$ are the same.
IV. The terminal points of $\vec{a}$ and $\vec{b}$ are the same.

Let $\vec{OA}=\vec{a}+2\vec{b}, \vec{OB}=3\vec{a}-\vec{b},$ and $\vec{OC}=2\vec{a}+k\vec{b}$ in the diagram below. If the three points $A, B,$ and $C$ lie on the line $l$ , which of the following is equal to $k$ ?

Details and assumptions:

Point $O$ does $\color{#D61F06}{\text{not}}$ lie on the line $l.$

\dfrac{2}{3}

\dfrac{1}{2}

\dfrac{1}{3}

\dfrac{3}{2}

Find the unit vector in the direction $(1,2,3).$

(1\hat{i})+(2\hat{j})+(3\hat{k})

\left(\frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}\right)

\left(\frac{1}{\sqrt{11}},\frac{2}{\sqrt{11}},\frac{3}{\sqrt{11}}\right)

\left(\frac{1}{\sqrt{15}},\frac{2}{\sqrt{15}},\frac{3}{\sqrt{15}}\right)

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