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A vector, 7 units from the origin, along the X axis, is added to vector 11 units from the origin along the Y axis. What is the resultant vector?
- a)3î + 8ĵ
- b)7î + 11ĵ
- c)11î + 7ĵ
- d)2î + 7ĵ
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A vector, 7 units from the origin, along the X axis, is added to vecto...
The vector 7 units from the origin and along X axis is 7î. The vector 11 units from the origin and along Y axis is 11ĵ. Hence the sum is 7î + 11ĵ.
Most Upvoted Answer
A vector, 7 units from the origin, along the X axis, is added to vecto...
Given Vectors:
- Vector along X-axis: 7 units (let's call this vector A)
- Vector along Y-axis: 11 units (let's call this vector B)
Finding Resultant Vector:
- To find the resultant vector, we need to add vectors A and B.
- Since vector A is along the X-axis and vector B is along the Y-axis, they are perpendicular to each other.
- Using the Pythagorean theorem, we can calculate the magnitude of the resultant vector:
- Magnitude = sqrt((7)^2 + (11)^2) = sqrt(49 + 121) = sqrt(170) ≈ 13.04 units
- Now, to find the direction of the resultant vector:
- tan(theta) = opposite/adjacent = 11/7
- theta ≈ arctan(11/7) ≈ 56.31 degrees
- Therefore, the resultant vector is 13.04 units at an angle of 56.31 degrees.
- Representing this in component form, we get:
- Resultant Vector = 7î + 11ĵ
Final Answer:
- Therefore, the correct resultant vector is 7î + 11ĵ, which is option B.
- Vector along X-axis: 7 units (let's call this vector A)
- Vector along Y-axis: 11 units (let's call this vector B)
Finding Resultant Vector:
- To find the resultant vector, we need to add vectors A and B.
- Since vector A is along the X-axis and vector B is along the Y-axis, they are perpendicular to each other.
- Using the Pythagorean theorem, we can calculate the magnitude of the resultant vector:
- Magnitude = sqrt((7)^2 + (11)^2) = sqrt(49 + 121) = sqrt(170) ≈ 13.04 units
- Now, to find the direction of the resultant vector:
- tan(theta) = opposite/adjacent = 11/7
- theta ≈ arctan(11/7) ≈ 56.31 degrees
- Therefore, the resultant vector is 13.04 units at an angle of 56.31 degrees.
- Representing this in component form, we get:
- Resultant Vector = 7î + 11ĵ
Final Answer:
- Therefore, the correct resultant vector is 7î + 11ĵ, which is option B.
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A vector, 7 units from the origin, along the X axis, is added to vector 11 units from the origin along the Y axis. What is the resultant vector?a)3î + 8b)7î + 11c)11î + 7d)2î + 7Correct answer is option 'B'. Can you explain this answer?
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A vector, 7 units from the origin, along the X axis, is added to vector 11 units from the origin along the Y axis. What is the resultant vector?a)3î + 8b)7î + 11c)11î + 7d)2î + 7Correct answer is option 'B'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about A vector, 7 units from the origin, along the X axis, is added to vector 11 units from the origin along the Y axis. What is the resultant vector?a)3î + 8b)7î + 11c)11î + 7d)2î + 7Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vector, 7 units from the origin, along the X axis, is added to vector 11 units from the origin along the Y axis. What is the resultant vector?a)3î + 8b)7î + 11c)11î + 7d)2î + 7Correct answer is option 'B'. Can you explain this answer?.
A vector, 7 units from the origin, along the X axis, is added to vector 11 units from the origin along the Y axis. What is the resultant vector?a)3î + 8b)7î + 11c)11î + 7d)2î + 7Correct answer is option 'B'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about A vector, 7 units from the origin, along the X axis, is added to vector 11 units from the origin along the Y axis. What is the resultant vector?a)3î + 8b)7î + 11c)11î + 7d)2î + 7Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vector, 7 units from the origin, along the X axis, is added to vector 11 units from the origin along the Y axis. What is the resultant vector?a)3î + 8b)7î + 11c)11î + 7d)2î + 7Correct answer is option 'B'. Can you explain this answer?.
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