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Let a and b be positive real numbers. Suppose  are adjacent sides of a parallelogram PQRS. Let  be the projection vectors of , respectively.  and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?
  • a)
    a + b = 4 
  • b)
    a – b = 2
  • c)
    The length of the diagonal PR of the parallelogram PQRS is 4 
  • d)
    is an angle bisector of the vectors 
Correct answer is option 'A,C'. Can you explain this answer?
Verified Answer
Let aand bbe positive real numbers. Supposeare adjacent sides of apara...



(a > 0, b > 0)  
similarly for a > b we will get a = b  
Now area of parallelogram = |(ai + bj) x ( ai - bj)|
= 2ab
∴ 2ab = 8  
ab = 4  ...(2)  
from (1) and (2)  
a = 2, b = 2 ∴ a + b = 4  option (A)
length of diagonal is 

so option (C) 
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Let aand bbe positive real numbers. Supposeare adjacent sides of aparallelogram PQRS. Letbe the projection vectors of,respectively.and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?a)a + b = 4b)a – b = 2c)The length of the diagonal PR of the parallelogram PQRS is 4d)is an angle bisector of the vectorsCorrect answer is option 'A,C'. Can you explain this answer?
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Let aand bbe positive real numbers. Supposeare adjacent sides of aparallelogram PQRS. Letbe the projection vectors of,respectively.and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?a)a + b = 4b)a – b = 2c)The length of the diagonal PR of the parallelogram PQRS is 4d)is an angle bisector of the vectorsCorrect answer is option 'A,C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let aand bbe positive real numbers. Supposeare adjacent sides of aparallelogram PQRS. Letbe the projection vectors of,respectively.and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?a)a + b = 4b)a – b = 2c)The length of the diagonal PR of the parallelogram PQRS is 4d)is an angle bisector of the vectorsCorrect answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let aand bbe positive real numbers. Supposeare adjacent sides of aparallelogram PQRS. Letbe the projection vectors of,respectively.and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?a)a + b = 4b)a – b = 2c)The length of the diagonal PR of the parallelogram PQRS is 4d)is an angle bisector of the vectorsCorrect answer is option 'A,C'. Can you explain this answer?.
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