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Vectors A and BareCollinear
- a)if they are in the same line
- b)if they are have equal magnitude
- c)if the direction cosines of one are negatives of the other
- d)if they are parallel to the same lineirrespective of their magnitudes and directions.
Correct answer is option 'D'. Can you explain this answer?
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Vectors A and BareCollineara)if they are in the same lineb)if they are...
Two vectors A and B are said to be collinear , if they are parallel to the same line irrespective of their magnitudes and directions.
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Vectors A and BareCollineara)if they are in the same lineb)if they are...
Introduction
When two vectors are parallel, it means that they have the same direction or are in the same line. In this question, we are given two vectors A and B and we need to determine if they are parallel to the same line, irrespective of their magnitudes and directions.
Explanation
To determine if two vectors are parallel to the same line, we need to compare their direction ratios or direction cosines.
a) Same Line
If two vectors A and B are in the same line, it means that they have the same direction. This implies that their direction ratios or direction cosines will be proportional to each other.
b) Equal Magnitude
If two vectors A and B have equal magnitudes, it means that their lengths are the same. However, this does not necessarily imply that they are in the same line or have the same direction. Magnitude only represents the length of a vector, not its direction.
c) Negative Direction Cosines
If the direction cosines of one vector are negatives of the other, it means that their directions are opposite to each other. This implies that the vectors are in the same line but have opposite directions.
d) Parallel to the Same Line
When we say that two vectors are parallel to the same line, irrespective of their magnitudes and directions, it means that they have the same direction cosines. Direction cosines represent the ratios of the components of a vector with respect to the axes. If the direction cosines of two vectors are the same, then they are parallel to the same line.
Conclusion
In this question, option D is the correct answer because it states that the vectors are parallel to the same line, irrespective of their magnitudes and directions. This means that their direction cosines are the same, indicating that they have the same ratios of components with respect to the axes.
When two vectors are parallel, it means that they have the same direction or are in the same line. In this question, we are given two vectors A and B and we need to determine if they are parallel to the same line, irrespective of their magnitudes and directions.
Explanation
To determine if two vectors are parallel to the same line, we need to compare their direction ratios or direction cosines.
a) Same Line
If two vectors A and B are in the same line, it means that they have the same direction. This implies that their direction ratios or direction cosines will be proportional to each other.
b) Equal Magnitude
If two vectors A and B have equal magnitudes, it means that their lengths are the same. However, this does not necessarily imply that they are in the same line or have the same direction. Magnitude only represents the length of a vector, not its direction.
c) Negative Direction Cosines
If the direction cosines of one vector are negatives of the other, it means that their directions are opposite to each other. This implies that the vectors are in the same line but have opposite directions.
d) Parallel to the Same Line
When we say that two vectors are parallel to the same line, irrespective of their magnitudes and directions, it means that they have the same direction cosines. Direction cosines represent the ratios of the components of a vector with respect to the axes. If the direction cosines of two vectors are the same, then they are parallel to the same line.
Conclusion
In this question, option D is the correct answer because it states that the vectors are parallel to the same line, irrespective of their magnitudes and directions. This means that their direction cosines are the same, indicating that they have the same ratios of components with respect to the axes.
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Vectors A and BareCollineara)if they are in the same lineb)if they are have equal magnitudec)if the direction cosines of one are negatives of the otherd)if they are parallel to the same lineirrespective of their magnitudes and directions.Correct answer is option 'D'. Can you explain this answer?
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