Vector Algebra

Which of the following statements about the dot product is always true?

1. The result is always a vector
2. The result is always a scalar
3. The result is always positive
4. The result is always equal to zero

If a = i + 2j and b = 2i + 4j, then the vectors are

1. Perpendicular
2. Parallel
3. Equal
4. Unit vectors

Two vectors are parallel if

1. Their dot product is zero
2. One vector is a scalar multiple of the other
3. Their magnitudes are equal
4. Their sum is zero

The cosine of the angle between two vectors a and b is given by

1. (a.b)/(|a||b|)
2. |a||b|/(a.b)
3. |a + b|
4. |a - b|

If a = 3i + 4j + 12k, then the magnitude of vector a is

1. 12
2. 13
3. 15
4. 17

If |a| = 5, |b| = 4, and the angle between them is 90 degrees, then |a.b| equals

1. 20
2. 10
3. 0
4. 1

The position vector of the point (2, -3, 4) is

1. 2i - 3j + 4k
2. 2i + 3j + 4k
3. -2i + 3j - 4k
4. i - 3j + 2k

Two vectors are perpendicular if

1. Their cross product is zero
2. Their dot product is zero
3. Their magnitudes are equal
4. Their sum is zero

If the angle between two non-zero vectors is 60 degrees, then their dot product is

1. |a||b|
2. (1/2)|a||b|
3. sqrt(3)|a||b|
4. 0

If a = 2i + 3j and b = 4i - j, then the dot product a.b is

1. 5
2. 8
3. 11
4. 13

The dot product of two perpendicular vectors is

1. 1
2. Equal to their magnitudes
3. 0
4. -1

If a = 5i - 2j and b = 3i + j, then a - b is

1. 2i - 3j
2. 8i - j
3. 2i + 3j
4. 8i + j

If a = 2i + 3j and b = i - j, then a + b equals

1. 3i + 2j
2. i + 4j
3. 3i - 2j
4. i + 2j

The unit vector in the direction of a = 6i + 8j is

1. (3/5)i + (4/5)j
2. 6i + 8j
3. (4/5)i + (3/5)j
4. (5/3)i + (5/4)j

The magnitude of the vector a = 3i + 4j is

1. 5
2. 7
3. 12
4. 25