Lesson J3-J4
J3-J4 Vector operations and position vectors Quiz: AQA Maths, Unit 10
20 questions
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Lesson J3-J4, Vector operations and position vectors: 20 multiple choice questions for the AQA Maths (7357), Unit 10: Vectors, written with Revision Ninja.
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The 20 questions
-
What is the position vector of point P with coordinates (x, y)?
- x - y
- x / y
- xy
- xi + yj
-
If points A and B have position vectors a and b, what is the vector AB?
- b - a
- (a + b)/2
- a + b
- a - b
-
What happens to vector v when multiplied by scalar k = -2?
- Doubled same direction
- Doubled and reversed
- Halved same direction
- Halved and reversed
-
Using the triangle law, where does the resultant vector a + b begin?
- Head of b
- Midpoint of a
- Tail of a
- Head of a
-
If A and B have position vectors a and b, what is the position vector of the midpoint of AB?
- (b - a)/2
- (a + b)/2
- a + b
- b - a
-
For a = (2, 3) and b = (5, -1), what is a + b?
- (7, 2)
- (3, -4)
- (7, 4)
- (10, -3)
-
For a = (1, 4) and b = (3, -2), what is 2a - b?
- (-1, 10)
- (-1, 6)
- (1, 10)
- (5, 6)
-
Points P(-2, 1) and Q(4, 9) are given. What is the distance PQ?
- 10
- sqrt(52)
- 14
- 7
-
What is the midpoint of the points A(-2, 1) and B(4, 9)?
- (1, 4)
- (2, 5)
- (3, 8)
- (1, 5)
-
Points A and B have position vectors (0, 0) and (6, 9). P lies on AB with AP:PB = 1:2. What is the position vector of P?
- (2, 3)
- (1, 1.5)
- (4, 6)
- (3, 4.5)
-
If a = (3, -4), what is the magnitude of 2a?
- 5
- 14
- 10
- 20
-
What is the unit vector parallel to (5, 12)?
- (1/5, 12/5)
- (5/12, 1)
- (5/13, 12/13)
- (13/5, 12/5)
-
Vectors (2, k) and (6, 9) are parallel. What is k?
- 3
- 9
- 1/3
- 6
-
If vector AB = (2, 4) and vector BC = (2, 4), what describes points A, B, and C?
- They are perpendicular
- They are collinear
- They form a triangle
- They are equidistant
-
If AB = b - a, what is BA?
- a + b
- b - a
- a - b
- -(a + b)
-
Vectors a = (1, 2) and b = (4, -2) are given. What is c = 2a - b?
- (6, -2)
- (-2, 6)
- (-2, 2)
- (2, 6)
-
What positive value of k makes |k(3, 4)| equal to 10?
- 1/2
- 5
- 2
- 10
-
Points P(2, -1) and Q(5, 3) are given. Point R satisfies PR = 2PQ. What are the coordinates of R?
- (8, 7)
- (6, 8)
- (4, -2)
- (11, 11)
-
Vectors a = 2i + 3j and b = i - j are given. What is 3a - 2b?
- 8i + 7j
- 4i + 7j
- 8i + 11j
- 4i + 11j
-
A line passes through points with position vectors a and b. Which vector equation gives the points on the line?
- r = a + t(b - a), for real t
- r = (a + b)t
- r = a - t(a + b)
- r = a + tb, for 0 <= t <= 1
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