Chapter 7 Vector Math 12th Class Punjab MCQ Tests
12th Class Math Chapter 7 MCQ Tests
Chapter 7 of 12th Class Math has 25 questions. If you take an online MCQ test, the system will randomly choose the questions. If you want to take the quiz by chapter then click the start test button.
Total Questions: 25
Total Marks: 25
Time: 25 Mins
Total Questions: 25
Total Marks: 25
Time: 25 Mins
25Min : 00 Sec Remaining
Question # 1
Find the scalar triple product of vectors → a = ⟨ 1 , 2 , 3 ⟩ , → b = ⟨ 1 , 1 , 1 ⟩ , → c = ⟨ 1 , 2 , 1 ⟩.
Question # 2
If a man walks 3 miles East, then 4 miles North, what is his final displacement (in miles)?
Question # 3
Mario programs his helicopter to fly at a target with a velocity (speed and direction) of → P . The direction of → P is due East and its speed is 6m / s . To Mario's dismay, the wind causes his helicopter to actually fly with a velocity → a and it misses its target. The direction of → a is 30 ∘ South of East and its speed is 5m / s . In what direction is the wind blowing?
Question # 4
Find the angle between two vectors → a = ⟨ 3 , 4 ⟩ and → b = ⟨ 4 , 3 ⟩.
Question # 5
(See the graph).
Question # 6
What is the sum of the vectors that point to the vertices of a cube centered at the origin (in 3-dim space)?
Question # 7
Find the volume of the parallelopiped for which the given vectors are three edges:
Question # 8
Calculate [ ( i − j ) × ( k − i ) ] ⋅ ( i + j ).
Question # 9
The segments AP, BQ and CR are the medians in the triangle ABC, then the sum of the vectors AP, BQ and CR is the _____ vector.
Question # 10
Which of the vectors ¯a = ⟨ 1 , 2 ⟩ , ¯b = ⟨ 4 , 8 ⟩ , ¯ c = ⟨ 5 , 9 ⟩ are collinear?
Question # 11
Projection of vector →A in direction of x-axis is represented by angle of _____.
Question # 12
Two forces 10N and 20N making an angle 30° and 60° will give a resultant force of _____.
Question # 13
Find the cross product of → a = ⟨ 1 , 2 , 3 ⟩ and → b = ⟨ 2 , 1 , − 2 ⟩.
Question # 14
Use the dot product to find the angle θ.
Question # 15
Mighty Casey hits two baseballs out of the park. The path of the first baseball can be described by the displacement (distance and direction) vector → b 1 = 100 ^ i + 10 ^ j . The path of the second baseball can be described by the displacement vector → b 2 = 90 ^ i − 20 ^ j . How far are the baseballs apart ?
Question # 16
Axes in three dimensional coordinate system divide plane in three spaces called _____.
Question # 17
P divides A P : P B in the ratio 1 : 2 , A P Bar :P B Bar = 1 : 2 to find the coordinates of P , if A ( 1 , 6 , 7 ) and B ( − 2 , 0 , − 2 ).
Question # 18
If → a × ^ i = 0 and → a × ^ j = 0 , then → a _____.
Question # 19
Find the vector → a if its length equal to 26 and direction cosines are cosα = 5 / 13 , cosβ = − 12 / 13.
Question # 20
If →a, →b and →c are three vectors, such that →a× →b = →a× →c, then:
Question # 21
What is ratio formula for two vectors.
Question # 22
Sum of all torques acting on a body is zero, this condition represents equilibrium's _____ condition.
Question # 23
Which of the vectors ¯a = ⟨ 1 , 2 , 3 ⟩ , ¯b = ⟨ 4 , 8 , 12 ⟩ , ¯ c = ⟨ 5 , 10 , 12 ⟩ are collinear?
Question # 24
Solve the:
Question # 25
Point A has coordinates ( 4 , 7 ) and point B has coordinates ( 6 , 2 ) . Mark M , the midpoint of AB. What is the position vector OM.
Total Questions
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Question # 1
Find the scalar triple product of vectors → a = ⟨ 1 , 2 , 3 ⟩ , → b = ⟨ 1 , 1 , 1 ⟩ , → c = ⟨ 1 , 2 , 1 ⟩.
Question # 2
If a man walks 3 miles East, then 4 miles North, what is his final displacement (in miles)?
Question # 3
Mario programs his helicopter to fly at a target with a velocity (speed and direction) of → P . The direction of → P is due East and its speed is 6m / s . To Mario's dismay, the wind causes his helicopter to actually fly with a velocity → a and it misses its target. The direction of → a is 30 ∘ South of East and its speed is 5m / s . In what direction is the wind blowing?
Question # 4
Find the angle between two vectors → a = ⟨ 3 , 4 ⟩ and → b = ⟨ 4 , 3 ⟩.
Question # 5
(See the graph).
Question # 6
What is the sum of the vectors that point to the vertices of a cube centered at the origin (in 3-dim space)?
Question # 7
Find the volume of the parallelopiped for which the given vectors are three edges:
Question # 8
Calculate [ ( i − j ) × ( k − i ) ] ⋅ ( i + j ).
Question # 9
The segments AP, BQ and CR are the medians in the triangle ABC, then the sum of the vectors AP, BQ and CR is the _____ vector.
Question # 10
Which of the vectors ¯a = ⟨ 1 , 2 ⟩ , ¯b = ⟨ 4 , 8 ⟩ , ¯ c = ⟨ 5 , 9 ⟩ are collinear?
Question # 11
Projection of vector →A in direction of x-axis is represented by angle of _____.
Question # 12
Two forces 10N and 20N making an angle 30° and 60° will give a resultant force of _____.
Question # 13
Find the cross product of → a = ⟨ 1 , 2 , 3 ⟩ and → b = ⟨ 2 , 1 , − 2 ⟩.
Question # 14
Use the dot product to find the angle θ.
Question # 15
Mighty Casey hits two baseballs out of the park. The path of the first baseball can be described by the displacement (distance and direction) vector → b 1 = 100 ^ i + 10 ^ j . The path of the second baseball can be described by the displacement vector → b 2 = 90 ^ i − 20 ^ j . How far are the baseballs apart ?
Question # 16
Axes in three dimensional coordinate system divide plane in three spaces called _____.
Question # 17
P divides A P : P B in the ratio 1 : 2 , A P Bar :P B Bar = 1 : 2 to find the coordinates of P , if A ( 1 , 6 , 7 ) and B ( − 2 , 0 , − 2 ).
Question # 18
If → a × ^ i = 0 and → a × ^ j = 0 , then → a _____.
Question # 19
Find the vector → a if its length equal to 26 and direction cosines are cosα = 5 / 13 , cosβ = − 12 / 13.
Question # 20
If →a, →b and →c are three vectors, such that →a× →b = →a× →c, then:
Question # 21
What is ratio formula for two vectors.
Question # 22
Sum of all torques acting on a body is zero, this condition represents equilibrium's _____ condition.
Question # 23
Which of the vectors ¯a = ⟨ 1 , 2 , 3 ⟩ , ¯b = ⟨ 4 , 8 , 12 ⟩ , ¯ c = ⟨ 5 , 10 , 12 ⟩ are collinear?
Question # 24
Solve the:
Question # 25
Point A has coordinates ( 4 , 7 ) and point B has coordinates ( 6 , 2 ) . Mark M , the midpoint of AB. What is the position vector OM.
Total Questions
12345678910111213141516171819202122232425
Math MCQ Test by Topics
- +7.1 Introduction
- +7.1.1 Geometric Interpretation of vector
- +7.1.2 Multiplication of Vector by a Scalar
- +7.1.3 Addition and Subtraction of Two Vectors
- +7.1.4 Position Vector
- +7.1.5 Vectors in a Plane
- +7.1.6 Properties of Magnitude of a Vector
- +7.1.7 Another notation for representing vectors in plane
- +7.1.8 A unit vector in the direction of another given vector
- +7.1.9 The Ratio Formula
- +7.1.10 Vector Geometry
- +7.1 Exercise
- +7.2 Introduction of vector in Space
- +7.2.1 Concept of a vector in space
- +7.2.2 Properties of Vectors
- +7.2.3 Another notation for representing vectors in space
- +7.2.4 Distance Between two Points in Space
- +7.2.5 Direction Angles and Direction Cosines of a Vector
- +7.2 Exercise
- +7.3 The Scalar Product of two Vectors
- +7.3.1 Deductions of the Important Results
- +7.3.2 Perpendicular (Orthogonal) Vectors
- +7.3.3 Properties of Dot Product
- +7.3.4 Analytical Expression of Dot Product u.v (Dot product of vectors in their components form)
- +7.3.5 Angle between two vectors
- +7.3.6 Projection of one Vector upon another Vector:
- +7.3 Exercise
- +7.4 The Cross Product or Vector Product of Two vectors
- +7.4.1 Derivation of useful results of cross products
- +7.4.2 Properties of Cross product
- +7.4.3 Analytical Expression of u x v (Determinant formula for u x v)
- +7.4.4 Parallel Vectors
- +7.4.5 Area of Parallelogram
- +7.4.6 Area of Triangle
- +7.4 Exercise
- +7.5 Scalar Triple Product of Vectors
- +7.5.1 Analytical Expression of u.(v x w)
- +7.5.2 The Volume of the Parallelepiped
- +7.5.3 The Volume of the Tetrahedron
- +7.5.4 Application of Vectors in Physics and Engineering
- +7.5 Exercise
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Updated on: 17-05-2026
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