How to find the perpendicular of a vector?
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1
Recall the formula for slope. The slope of any given line or line segment is calculated by dividing the vertical change (or the “rise”) by the horizontal change (the “run”).
2
Read the components of the given vector. A vector can be written in component form as (i,j). In this form, the first coefficient i represents the horizontal component of the vector, or the \Delta x. The second coefficient j represents the vertical component of the vector, or the \Delta y.
3
Calculate the slope. To find the slope, fill in the vector components into the formula for the slope. Specifically, you will divide the j component by the i component
4
Recall the geometric definition of perpendicular slopes. Two lines (including lines, line segments, or vectors) are perpendicular to each other if their slopes are negative reciprocals
5
Identify the reciprocal of the vector slope. After you have calculated the slope of your vector, find the reciprocal of that slope
6
Find the negative reciprocal. If the slope of the original vector is positive, then the slope of the perpendicular vector will have to be negative. Conversely, if the slope of the original vector is negative, then the slope of the perpendicular vector will be positive.
7
Write the new vector in component form. Knowing the slope is almost the final step. You then need just to rewrite the vector in its component form, using the “rise” and “run” components
Recall the formula for slope. The slope of any given line or line segment is calculated by dividing the vertical change (or the “rise”) by the horizontal change (the “run”).
2
Read the components of the given vector. A vector can be written in component form as (i,j). In this form, the first coefficient i represents the horizontal component of the vector, or the \Delta x. The second coefficient j represents the vertical component of the vector, or the \Delta y.
3
Calculate the slope. To find the slope, fill in the vector components into the formula for the slope. Specifically, you will divide the j component by the i component
4
Recall the geometric definition of perpendicular slopes. Two lines (including lines, line segments, or vectors) are perpendicular to each other if their slopes are negative reciprocals
5
Identify the reciprocal of the vector slope. After you have calculated the slope of your vector, find the reciprocal of that slope
6
Find the negative reciprocal. If the slope of the original vector is positive, then the slope of the perpendicular vector will have to be negative. Conversely, if the slope of the original vector is negative, then the slope of the perpendicular vector will be positive.
7
Write the new vector in component form. Knowing the slope is almost the final step. You then need just to rewrite the vector in its component form, using the “rise” and “run” components
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