Question
What are the different types of vectors?
✓
Answer
1. Equal vectors:
Two vectors A and B are said to be equal when they have equal magnitude and same direction and represent the same physical quantity
(a) Collinear vectors:
Col-linear vectors are those which act along the same line. The angle between them can be 0° or 180°.
(i) Parallel vectors:
If two vectors A and B act in the same direction along the same line or on parallel lines, then the angle between them is 0°. Geometrical representation of parallel vectors.
(ii) Anti-parallel vectors:
Two vectors A and B are said to be anti – parallel when they are in opposite directions along the same line or on parallel lines. Then the angle between them is 180°.
2. Unit vector:
A vector divided by its magnitude is a unit vector. The unit vector for $\overrightarrow{ A }$ is denoted by $\widehat{A}$. It has a magnitude equal to unity or one.
Since, $\widehat{A}=\frac{\bar{A}}{A}$ we can write $\overrightarrow{ A }= A \widehat{A}$
Thus, we can say that the unit vector specifies only the direction of the vector quantity.
3. Orthogonal unit vectors:
Let $\hat{i}, \hat{j}$ and $\hat{k}$ be three unit vectors which specify the directions along positive $x$-axis, positive $y$ axis and positive $z$-axis respectively. These three unit vectors are directed perpendicular to each other, the angle between any two of them is $90^{\circ} . \hat{i}, \hat{j}$ and $\hat{k}$ and are examples of orthogonal vectors. Two vectors which are perpendicular to each other are called orthogonal vectors as shown in the figure.
Two vectors A and B are said to be equal when they have equal magnitude and same direction and represent the same physical quantity
(a) Collinear vectors:
Col-linear vectors are those which act along the same line. The angle between them can be 0° or 180°.
(i) Parallel vectors:
If two vectors A and B act in the same direction along the same line or on parallel lines, then the angle between them is 0°. Geometrical representation of parallel vectors.
(ii) Anti-parallel vectors:
Two vectors A and B are said to be anti – parallel when they are in opposite directions along the same line or on parallel lines. Then the angle between them is 180°.
2. Unit vector:
A vector divided by its magnitude is a unit vector. The unit vector for $\overrightarrow{ A }$ is denoted by $\widehat{A}$. It has a magnitude equal to unity or one.
Since, $\widehat{A}=\frac{\bar{A}}{A}$ we can write $\overrightarrow{ A }= A \widehat{A}$
Thus, we can say that the unit vector specifies only the direction of the vector quantity.
3. Orthogonal unit vectors:
Let $\hat{i}, \hat{j}$ and $\hat{k}$ be three unit vectors which specify the directions along positive $x$-axis, positive $y$ axis and positive $z$-axis respectively. These three unit vectors are directed perpendicular to each other, the angle between any two of them is $90^{\circ} . \hat{i}, \hat{j}$ and $\hat{k}$ and are examples of orthogonal vectors. Two vectors which are perpendicular to each other are called orthogonal vectors as shown in the figure.
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