Geometry

Properties of a Vector

Vector Terminology

         

Which of the following is a vector quantity?

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

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

Details and assumptions:

  • O is the intersection point of the three diagonal lines.

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

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

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

Details and assumptions:

  • Point OO does not\color{red}{\text{not}} lie on the line l.l.

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

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