## 1. What does a vector represent?

### Answer:

### Explanation:

By definition, a vector has both magnitude (how much) and direction (which way).

## 2. If two vectors are parallel, their cross product is:

### Answer:

### Explanation:

The cross product of parallel vectors is zero since they don't enclose any area.

## 3. The dot product of two perpendicular vectors is:

### Answer:

### Explanation:

Dot product of two perpendicular vectors is zero since cos(90°) is 0.

## 4. If |a| = 3 and |b| = 4, what is the maximum value of the dot product a.b?

### Answer:

### Explanation:

Maximum value of a.b is |a||b|cos(0°) = |a||b|.

## 5. A unit vector is a vector with magnitude:

### Answer:

### Explanation:

A unit vector has a magnitude of one.

## 6. Which of the following is not a scalar quantity?

### Answer:

### Explanation:

Velocity has both magnitude and direction, making it a vector.

## 7. If a and b are two vectors, then a x (b x a) is:

### Answer:

### Explanation:

Using vector triple product rule, a x (b x a) = (a.b)a – (a.a)b = -|a|^2b + (a.b)a. When a and b are orthogonal, the result is -a.

## 8. What does the cross product of two vectors result in?

### Answer:

### Explanation:

The cross product of two vectors gives another vector.

## 9. If the vectors a and b are collinear, then:

### Answer:

### Explanation:

For collinear vectors, their cross product is zero.

## 10. Which operation on two vectors produces a scalar?

### Answer:

### Explanation:

The dot product of two vectors results in a scalar.

## 11. If a vector has zero magnitude, it is called:

### Answer:

### Explanation:

A vector with no magnitude and arbitrary direction is a zero vector.

## 12. The vectors a, b, and c are said to be coplanar if:

### Answer:

### Explanation:

If the scalar triple product is zero, the vectors are coplanar.

## 13. If a.b = a.c and |b| = |c|, then:

### Answer:

### Explanation:

Given conditions imply b – c is perpendicular to a.

## 14. The angle between the vectors i and j is:

### Answer:

### Explanation:

i and j are perpendicular unit vectors.

## 15. If |a| = 5 and |b| = 7, and the angle between them is 60°, then a.b is:

### Answer:

### Explanation:

a.b = |a||b|cos(60°) = 5*7*0.5 = 21.

## 16. If the vectors a and b are orthogonal, their dot product is:

### Answer:

### Explanation:

Dot product of orthogonal vectors is zero since the angle between them is 90°.

## 17. The magnitude of the vector 3i – 4j is:

### Answer:

### Explanation:

Square root of (3^2 + (-4)^2) is 5.

## 18. The projection of a vector a on b is given by:

### Answer:

### Explanation:

The projection is the component of a in the direction of b.

## 19. If a + b = c, then b is:

### Answer:

### Explanation:

Rearranging the given equation, we get b = c – a.

## 20. The unit vector in the direction of the vector 4i + 3j is:

### Answer:

### Explanation:

To find the unit vector, divide each component by the magnitude of the vector.