Vectors Practice Questions
Thanaweya Amma (Egypt) · Thanaweya Mathematics · 143 free MCQs with instant results and detailed explanations.
143
Total
50
Easy
71
Medium
22
Hard
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Sample Questions from Vectors
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
If vector C = (1, 2) and vector D = (3, 4), what is the magnitude of the resultant vector R = C + D?
A.
5
B.
6
C.
7
D.
โ10
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Correct Answer: B
The resultant vector R = C + D = (1 + 3, 2 + 4) = (4, 6). The magnitude is calculated as โ(4ยฒ + 6ยฒ) = โ(16 + 36) = โ52 = 6.
Q2
Easy
What is the magnitude of the vector A = (3, 4)?
A.
5
B.
7
C.
12
D.
10
Show Answer & Explanation
Correct Answer: A
The magnitude of a vector A = (x, y) is calculated using the formula โ(xยฒ + yยฒ). Here, โ(3ยฒ + 4ยฒ) = โ(9 + 16) = โ25 = 5.
Q3
Easy
If vector B = (2, -3) and vector C = (4, 1), what is the result of vector B + vector C?
A.
(6, -2)
B.
(2, -4)
C.
(0, -2)
D.
(4, -2)
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Correct Answer: A
To add vectors B and C, add their respective components: B + C = (2 + 4, -3 + 1) = (6, -2).
Q4
Medium
Given two vectors A = 5i - 3j and B = 2i + j, which statement is true regarding their cross product?
A.
A ร B is a scalar.
B.
A ร B is a vector perpendicular to both A and B.
C.
A ร B equals zero.
D.
A ร B is in the direction of vector A.
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Correct Answer: B
The cross product of two vectors is always a vector that is perpendicular to the plane formed by the original vectors.
Q5
Medium
If vectors A = 4i + 5j and B = -2i + 3j, what is the resultant vector R = A + B?
A.
2i + 8j
B.
6i + 2j
C.
2i + 2j
D.
1i + 8j
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Correct Answer: A
The resultant vector R is found by adding corresponding components: R = (4 - 2)i + (5 + 3)j = 2i + 8j.
Q6
Medium
If the magnitude of vector A is 10 units and the angle with the x-axis is 60 degrees, what are the components of vector A?
A.
5i + 5โ3 j
B.
10i + 0j
C.
10i + 10j
D.
5โ3 i + 5 j
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Correct Answer: D
The components are calculated using A_x = |A| * cos(ฮธ) and A_y = |A| * sin(ฮธ). Thus, A_x = 10 * 0.5 = 5โ3 and A_y = 10 * (โ3/2) = 5.
Q7
Medium
Which of the following vectors is orthogonal to the vector A = 4i + 3j?
A.
3i - 4j
B.
4i + 3j
C.
i + j
D.
-3i + 4j
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Correct Answer: A
Two vectors are orthogonal if their dot product is zero. Here, (4)(3) + (3)(-4) = 12 - 12 = 0.
Q8
Hard
If vectors A and B are perpendicular and their magnitudes are |A| = 8 and |B| = 6, what is the magnitude of their cross product A ร B?
A.
48
B.
24
C.
12
D.
30
Show Answer & Explanation
Correct Answer: A
The magnitude of the cross product of two perpendicular vectors is given by |A ร B| = |A| * |B| * sin(90ยฐ). Therefore, |A ร B| = 8 * 6 * 1 = 48.
Q9
Hard
Given two vectors A = 3i + 4j and B = -2i + j, calculate the angle ฮธ between the vectors A and B.
A.
90 degrees
B.
60 degrees
C.
120 degrees
D.
75 degrees
Show Answer & Explanation
Correct Answer: C
To find the angle between two vectors, we use the formula cos(ฮธ) = (AยทB) / (|A| |B|). The dot product AยทB = (3)(-2) + (4)(1) = -6 + 4 = -2. The magnitudes |A| = 5 and |B| = โ5. Thus, cos(ฮธ) = -2 / (5โ5). This implies ฮธ = 120 degrees, as the cosine of this angle is negative.
Q10
Hard
If vector C = 2i - 3j + k is reflected across the plane defined by the equation x + 2y + 3z = 0, what is the resulting vector D?
A.
2i - 6j + 3k
B.
2i + 6j - 3k
C.
-2i + 3j - k
D.
2i + 3j + 6k
Show Answer & Explanation
Correct Answer: B
To reflect vector C across the plane, we first find the normal vector of the plane, which is (1, 2, 3). The reflection formula gives us D = C - 2(Cยทn)n/|n|^2. After substituting the appropriate values and calculations, we get the resultant vector D = 2i + 6j - 3k.
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Vectors โ Thanaweya Amma (Egypt) Thanaweya Mathematics Practice Questions Online
This page contains 143 practice MCQs for the chapter Vectors in Thanaweya Amma (Egypt) Thanaweya Mathematics. The questions are organized by difficulty โ 50 easy, 71 medium, 22 hard โ so you can choose the right level for your preparation.
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