A vector for which is called a unit vector, and is denoted as . is the unit vector in the direction of the positive -axis, and is the unit vector in the direction of the positive -axis. If and are both scalar values, then is a vector with magnitude in the direction of is the vector with magnitude in the direction of is the vector with magnitude in the opposite direction of is the vector with magnitude in the direction of is the component form of the resultant vector that extends units horizontally (to the left if and to the right if ) and units vertically (up if or down if ). and are the components of . A vector that has an initial point at the origin is called a position vector, and as a consequence the terminal point of is . A vector whose initial point is not at the origin is called a displacement vector. Suppose that is a displacement vector with initial point , not necessarily the origin, and terminal point . If , then is equal to the position vector . Example 2 Find the displacement vector if and . – If and , then: if and only if and . Just like with polar complex notation, if , then and the direction of is or , depending on which quadrant the corresponding position vector would terminate in. Likewise, a vector with magnitude in the direction can be written as . Example 3 If and , find (a) and (b) . –
A vector for which is called a unit vector, and is denoted as . is the unit vector in the direction of the positive -axis, and is the unit vector in the direction of the positive -axis. If and are both scalar values, then is a vector with magnitude in the direction of is the vector with magnitude in the direction of is the vector with magnitude in the opposite direction of is the vector with magnitude in the direction of is the component form of the resultant vector that extends units horizontally (to the left if and to the right if ) and units vertically (up if or down if ). and are the components of . A vector that has an initial point at the origin is called a position vector, and as a consequence the terminal point of is . A vector whose initial point is not at the origin is called a displacement vector. Suppose that is a displacement vector with initial point , not necessarily the origin, and terminal point . If , then is equal to the position vector . Example 2 – Find the displacement vector if and . If and , then: if and only if and . Just like with polar complex notation, if , then and the direction of is or , depending on which quadrant the corresponding position vector would terminate in. Likewise, a vector with magnitude in the direction can be written as . Example 3 – If and , find (a) and (b) .