# Worksheet: Parallel and Perpendicular Vectors in Space

In this worksheet, we will practice recognizing parallel and perpendicular vectors in space.

Q1:

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.

• Atrue
• Bfalse

Q2:

Given that , , and , find the relation between and .

• A
• B
• C
• D

Q3:

Given that , , and , where and are two perpendicular unit vectors, find the value of .

Q4:

Suppose , , , and , find .

• A
• B
• C
• D

Q5:

Given the two vectors and , determine whether these two vectors are parallel, perpendicular, or otherwise.

• Aparallel
• Bperpendicular
• Cotherwise

Q6:

Find the values of and so that vector is parallel to vector .

• A,
• B,
• C,
• D,

Q7:

In the figure, is perpendicular to the plane , which contains the points , , , and . If and , find the area of . • A1,386
• B3,272.5
• C3,060
• D1,530

Q8:

Which of the following vectors is not perpendicular to the line whose direction vector is ?

• A
• B
• C
• D

Q9:

If the straight line is perpendicular to , and , find .

Q10:

If the straight line is parallel to , find .

Q11:

If the two straight lines and are perpendicular, find .

• A
• B
• C
• D

Q12:

Given that and satisfy , and . How are the two vectors related?

• Aperpendicular
• Bparallel