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If 2î + 4ĵ - 5k̂ and î + 2ĵ + 3k̂ are two different sides of rhombus. Find the length of diagonals.
- a)7, √69
- b)6, √59
- c)5 √65
- d)8, √45
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If 2i + 4j - 5k and i + 2j + 3k are two different sides of rhombus. Fi...
If aî + bĵ + ck̂ and pî + qĵ + rk̂ are 2 different sides of the rhombus.
Suppose 
= aî+bĵ+ck̂ and B = 
= pî+qĵ+rk̂
= aî+bĵ+ck̂ and B = = pî+qĵ+rk̂Then anyone diagonal of the rhombus is given by 
The other diagonal is given by 
The magnitude of the vector 
The magnitude of the vector diagonal D1
D1 = 7
The other diagonal is given by 
D2 = - 1î - 2ĵ + 8k̂
The magnitude of the vector diagonal D2
∴ The length of diagonals of a rhombus is 7 and √69.
Most Upvoted Answer
If 2i + 4j - 5k and i + 2j + 3k are two different sides of rhombus. Fi...
If aî + bĵ + ck̂ and pî + qĵ + rk̂ are 2 different sides of the rhombus.
Suppose = aî+bĵ+ck̂ and B = = pî+qĵ+rk̂
= aî+bĵ+ck̂ and B = = pî+qĵ+rk̂Then anyone diagonal of the rhombus is given by
The other diagonal is given by
The magnitude of the vector
The magnitude of the vector diagonal D1
D1 = 7
The other diagonal is given by
D2 = - 1î - 2ĵ + 8k̂
The magnitude of the vector diagonal D2
∴ The length of diagonals of a rhombus is 7 and √69.
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If 2i + 4j - 5k and i + 2j + 3k are two different sides of rhombus. Fi...
To find the length of the diagonals of the rhombus, we need to find the magnitude of the vectors 2i+4j-5k and i+2j+3k.
The magnitude of a vector is given by the square root of the sum of the squares of its components.
For the first vector, the magnitude is:
√((2^2) + (4^2) + (-5^2)) = √(4 + 16 + 25) = √45
For the second vector, the magnitude is:
√((1^2) + (2^2) + (3^2)) = √(1 + 4 + 9) = √14
So the length of the diagonals of the rhombus are √45 and √14.
However, the answer choices provided do not match these values. Therefore, the given answer choices are incorrect.
The magnitude of a vector is given by the square root of the sum of the squares of its components.
For the first vector, the magnitude is:
√((2^2) + (4^2) + (-5^2)) = √(4 + 16 + 25) = √45
For the second vector, the magnitude is:
√((1^2) + (2^2) + (3^2)) = √(1 + 4 + 9) = √14
So the length of the diagonals of the rhombus are √45 and √14.
However, the answer choices provided do not match these values. Therefore, the given answer choices are incorrect.
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If 2i + 4j - 5k and i + 2j + 3k are two different sides of rhombus. Find the length of diagonals.a)7, √69b)6, √59c)5 √65d)8, √45Correct answer is option 'A'. Can you explain this answer?
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