MCQ on Addition Subtraction of Vectors

A vector was just employed when someone told you to toss a ball twice as hard and to the left. A vector was just utilized when someone told you to travel northeast for roughly five miles. A vector quantity is any quantity that has to be completely characterized by defining its magnitude and direction. We use the term magnitude to describe the size of a quantity, such as length or strength. By direction, we mean the direction in which the vector is heading or directed, such as left or right, north, south, east or west, or even up or down. 1. When two vectors are added together, we obtain- a) a vector b) a scalar c) a number d) an operation. Answer- a Explanation- When two vectors are added together, the result is a vector. Subtraction and cross multiplication are the same. Only when two vectors are combined using the dot product method do we receive a scalar. 2. Adding 2î + 7 ĵ and î + ĵ gives- a) 3î + 8 ĵ b) î + 35 c) î + 8ĵ d) 2î + 7ĵ Answer- a Explanation- When you add 2î + 7 to î + ĵ, you obtain the matching components. As a result, the solution is 3î + 8j. 3. If you subtract 2î + 7 ĵ from î + ĵ you get- a) –î – 6ĵ b) 3î + 8ĵ c) î + 6ĵ d) 7ĵ Answer- a Explanation- The matching components are subtracted when 2î + 7ĵ  is subtracted from î +ĵ . As a result, the solution is -î – 6ĵ 4. When you add î + 77ĵ and 7î + ĵ, you get- a) 8î + 78ĵ b) 0î + 76ĵ c) î + 74ĵ d) 78î + 8ĵ Answer- a Explanation- The necessary components are added when î + 77ĵ  is added to 7î+ ĵ. As a result, the solution is 8î + 78ĵ. 5. The magnitude of the resultant vector is equal to, when two vectors in the same direction are combined- a) Sum of the vectors’ magnitudes b) Difference of the vectors’ magnitudes c) Product of the vectors’ magnitudes d) Sum of the roots of the vectors’ magnitudes Answer- a Explanation- The lengths will be added when one vector is added to the other in the same direction. The length of the resulting vector will equal the length of the resultant vector. The magnitude of the vector is measured in length. As a consequence, the magnitudes add together to yield the resulting vector’s magnitude. 6. Along the X axis, a vector 7 units from the origin is added to a vector 11 units from the origin along the Y axis. What does the generated vector look like? a) 3î + 8ĵ b) 7î + 11ĵ c) 11î + 7ĵ Answer- b Explanation- 7î is a vector that is 7 units from the origin and runs along the X axis. The vector 11 is 11ĵ units away from the origin and along the Y axis. As a result, the total is 7î + 11ĵ 7. The unit vector along the vector 4î + 3 is- a) (4î + 3ĵ)/5 b) 4î + 3ĵ c) (4î + 3ĵ)/6 d) (4î + 3ĵ) Answer –a Explanation- By dividing the current vector by its magnitude, a unit vector along 4î + 3ĵ is produced. The provided vector has a magnitude of 5. As a result, the unit vector needed is (4î + 3ĵ)/5. 8. The perpendicular unit vector to the vector 4î + 3ĵ a) ĵ b) î c) 4î + 3ĵ d) z^ Answer- d Explanation- Any two vectors that are perpendicular to each other have a dot product of 0. Except for z, the dot product of all vectors in the choices with 4î + 3ĵ is non-zero. As a result, z is perpendicular  to the specified vector. 9. A vector is added  to  the vector 40î + 30ĵ. As a consequence, the solution is 15î + 3ĵ , the unknown vector is- a) -25î – 27ĵ b) 25î + 27ĵ c) -25î + 27ĵ d) 25î – 27ĵ Answer – a 10. An example of calculating relative velocity is- a) Vector addition b) Vector subtraction c) Vector multiplication d) Vector division Answer- b Explanation- Vector V_R = Vector V_A – Vector V_B is the formula for relative velocity. Vector subtraction is used to find relative velocity. In reality, vector subtraction is required to determine the relative value of any vector quantity. 11. Along the X axis, a vector 5 units from the origin is added to a vector 2 units from the origin along the Y axis. What does the generated vector look like? a) 3î + 8ĵ b) 5î + 2ĵ c) 2î + 5ĵ d) 2î + 7ĵ Answer- b Explanation- 5î is a vector that is 5 units from the origin and runs along the X axis. 2 is the vector 2 units away from the origin and along the Y axis. As a result, the total is 5î + 2 ĵ 12. On the X axis, a vector 14 units from the origin is added to a vector 16 units from the origin on the Z axis. What does the generated vector look like? a) 3î + 8z^ b) 14î + 16z^ c) 16î + 14z^ d) 2î + 7z^ Answer- b Explanation- The vector 14î is 14 units from the origin and along the X axis. 16z is a vector 16 units from the origin and along the Y axis. As a result, the total is 14î + 16z ^. 13. An individual goes 10 kilometres north and 20 kilometres east. What will the distance from the starting location be? a) 20 kilometres b) 22.36 kilometres c) 30 kilometres d) 32.36 kilometres Answer- b 14. Two force’s vector sums are perpendicular to their vector differences. In such instance, the forces- a) Have the same magnitude as each other. b) Do not have the same magnitude as each other. c) It’s impossible to know ahead of time. d) They are on a perpendicular with one another. Answer- d