Worksheet: Parallel and Perpendicular Vectors in Space
In this worksheet, we will practice recognizing parallel and perpendicular vectors in space.
Determine whether the following is true or false: If the component of a vector in the direction of another vector is zero, then the two are parallel.
Given that , , and , find the relation between and .
Given that , , and , where and are two perpendicular unit vectors, find the value of .
Suppose , , , and , find .
Given the two vectors and , determine whether these two vectors are parallel, perpendicular, or otherwise.
In the figure, is perpendicular to the plane , which contains the points , , , and . If and , find the area of .
Which of the following vectors is not perpendicular to the line whose direction vector is ?
If the straight line is perpendicular to , and , find .
If the straight line is parallel to , find .
If the two straight lines and are perpendicular, find .
Given that and satisfy , and . How are the two vectors related?