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What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?
- a)It is either in the 1st quadrant or in 2nd quadrant
- b)It is either in the 1st quadrant or in 3rd quadrant
- c)It is either in the 1st quadrant or in 4th quadrant
- d)Only in the 1st quadrant
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What is the direction of the resultant vector if two vectors having eq...
If one is heading towards positive X-axis and the other is in the other direction opposite to the first one, with both having the same length and having an angle between them being obtuse, means that the direction is to be in the direction of either 1st quadrant or in the 4th quadrant.
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What is the direction of the resultant vector if two vectors having eq...
Solution:
Given, two vectors have the same length. One vector is parallel to the positive x-axis and the other vector is making 165 degrees with it and heading in the opposite direction of the first one.
Let's draw the vectors to understand the given information.
From the above diagram, we can see that the angle between the two vectors is 165 - 180 = -15 degrees.
To find the direction of the resultant vector, we need to find the sum of two vectors.
Let Vector A be parallel to the x-axis and Vector B be making 165 degrees with it and heading in the opposite direction of that of the first one.
Vector A can be represented as (a, 0) and Vector B can be represented as (-b cos 15, -b sin 15).
The sum of two vectors is Vector A + Vector B = (a - b cos 15, -b sin 15)
From the above equation, we can see that the x-component of the resultant vector is a - b cos 15 which is positive if a > b cos 15 and negative if a < b="" cos="" />
Similarly, the y-component of the resultant vector is negative because the angle of Vector B is in the fourth quadrant.
Therefore, the direction of the resultant vector is either in the first quadrant or in the fourth quadrant.
Hence, the correct option is (c) It is either in the 1st quadrant or in the 4th quadrant.
Given, two vectors have the same length. One vector is parallel to the positive x-axis and the other vector is making 165 degrees with it and heading in the opposite direction of the first one.
Let's draw the vectors to understand the given information.
From the above diagram, we can see that the angle between the two vectors is 165 - 180 = -15 degrees.
To find the direction of the resultant vector, we need to find the sum of two vectors.
Let Vector A be parallel to the x-axis and Vector B be making 165 degrees with it and heading in the opposite direction of that of the first one.
Vector A can be represented as (a, 0) and Vector B can be represented as (-b cos 15, -b sin 15).
The sum of two vectors is Vector A + Vector B = (a - b cos 15, -b sin 15)
From the above equation, we can see that the x-component of the resultant vector is a - b cos 15 which is positive if a > b cos 15 and negative if a < b="" cos="" />
Similarly, the y-component of the resultant vector is negative because the angle of Vector B is in the fourth quadrant.
Therefore, the direction of the resultant vector is either in the first quadrant or in the fourth quadrant.
Hence, the correct option is (c) It is either in the 1st quadrant or in the 4th quadrant.
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What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?a)It is either in the 1st quadrant or in 2nd quadrantb)It is either in the 1st quadrant or in 3rd quadrantc)It is either in the 1st quadrant or in 4thquadrantd)Only in the 1st quadrantCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?a)It is either in the 1st quadrant or in 2nd quadrantb)It is either in the 1st quadrant or in 3rd quadrantc)It is either in the 1st quadrant or in 4thquadrantd)Only in the 1st quadrantCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?a)It is either in the 1st quadrant or in 2nd quadrantb)It is either in the 1st quadrant or in 3rd quadrantc)It is either in the 1st quadrant or in 4thquadrantd)Only in the 1st quadrantCorrect answer is option 'C'. Can you explain this answer?.
What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?a)It is either in the 1st quadrant or in 2nd quadrantb)It is either in the 1st quadrant or in 3rd quadrantc)It is either in the 1st quadrant or in 4thquadrantd)Only in the 1st quadrantCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?a)It is either in the 1st quadrant or in 2nd quadrantb)It is either in the 1st quadrant or in 3rd quadrantc)It is either in the 1st quadrant or in 4thquadrantd)Only in the 1st quadrantCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?a)It is either in the 1st quadrant or in 2nd quadrantb)It is either in the 1st quadrant or in 3rd quadrantc)It is either in the 1st quadrant or in 4thquadrantd)Only in the 1st quadrantCorrect answer is option 'C'. Can you explain this answer?.
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