
The rectangular components of a vector lying in the plane are 1 and . If coordinate system turned by , they are and 4 respectively the value of is:
A) 2
B) 4
C)
D) 7
Answer
492k+ views
Hint:
First, we will assume that the components after rotation be and respectively, such that we have and . Then we will find these values from the problem and then substitute the values in the assumed expression to find the value of .
Complete step by step solution:
We are given that the rectangular components of a vector lying in plane are 1 and .
Let us assume that the components after rotation be and respectively, such that we have
Since we are given that when , the coordinates are and 4.
Finding the value of , , and , we get
Substituting these above values , and in the equation for , we get
Using the value of and in the above equation, we get
Substituting these above values , and in the equation for , we get
Using the value of and in the above equation, we get
Multiplying the above equation by 2 on both sides, we get
Adding the above equation with 1 on both sides, we get
Taking common from the right hand side of the above equation, we get
Dividing the above equation by on both sides, we get
Rationalizing the left hand side of the above equation by multiplying with numerator and denominator, we get
Subtracting the above equation by 1 on both sides, we get
Hence, option B is correct.
Note:
We need to know that rectangular components are from a vector, one for the –axis and the second one for the –axis. Students should use the values of trigonometric functions really carefully. Some angles can also be resolved along with these vectors. If is a vector then its component is and its component is .
First, we will assume that the components after rotation be
Complete step by step solution:
We are given that the rectangular components of a vector lying in
Let us assume that the components after rotation be
Since we are given that when
Finding the value of
Substituting these above values
Using the value of
Substituting these above values
Using the value of
Multiplying the above equation by 2 on both sides, we get
Adding the above equation with 1 on both sides, we get
Taking
Dividing the above equation by
Rationalizing the left hand side of the above equation by multiplying
Subtracting the above equation by 1 on both sides, we get
Hence, option B is correct.
Note:
We need to know that rectangular components are from a vector, one for the
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