Free Rectangular Components MCQs with Answers

1. A vector of magnitude 20 N acts at 30 degrees above the horizontal. Its horizontal component is

• A. 10 N
• B. 20 N
• C. 17.3 N
• D. 11.5 N

Explanation: The horizontal component is 20 cos 30, and cos 30 is 0.866, so the component is 17.3 N. The vertical component is 20 sin 30, which is 10 N, and that is the value offered as the distractor. Note that the components are always smaller than the vector itself, which is a quick sanity check.

2. If a vector has equal rectangular components, it makes an angle with the x axis of

• A. 30 degrees
• B. 45 degrees
• C. 60 degrees
• D. 90 degrees

Explanation: The angle is given by the inverse tangent of the ratio of the y component to the x component, and when the two are equal that ratio is 1, whose inverse tangent is 45 degrees. Each component then has magnitude equal to the vector divided by the square root of 2. At 90 degrees the x component would be zero rather than equal to the y component.

3. A unit vector has

• A. magnitude one and specifies direction only
• B. zero magnitude
• C. magnitude equal to the vector it came from
• D. no direction

Explanation: Dividing any vector by its own magnitude gives a unit vector along the same line, which carries the direction information with the size stripped away. The unit vectors i, j and k along the three axes are used to write any vector in component form. A null vector, by contrast, has zero magnitude and an undefined direction.

4. If A is 3i + 4j, its magnitude is

• A. 7
• B. 5
• C. 12
• D. 25

Explanation: The magnitude is the square root of the sum of the squares of the components, so the square root of (9 plus 16), which is the square root of 25, that is 5. Adding the components to get 7 ignores that they are perpendicular. The value 25 is the square of the magnitude, quoted before taking the root.