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If vectors (i+j+k),(5i+3j-3k) and (2i+5j+9k) are the position vectors of vertices of any triangle then its perimeter is
- a)15+√157
- b)15-√157
- c)√15-√157
- d)√15+√157
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If vectors (i+j+k),(5i+3j-3k) and (2i+5j+9k) are the position vectors ...
Given vectors are the position vectors of vertices of a triangle.
To find the perimeter of the triangle, we need to find the lengths of its sides.
Length of a side of the triangle = magnitude of the difference of the position vectors of its endpoints.
Therefore,
Length of first side = ||(5i 3j-3k) - (i j k)|| = ||4i 2j - 4k|| = 4√6
Length of second side = ||(2i 5j 9k) - (i j k)|| = ||i 4j 8k|| = 9
Length of third side = ||(2i 5j 9k) - (5i 3j-3k)|| = ||-3i 8j 12k|| = 13
Perimeter of the triangle = sum of the lengths of its sides = 4√6 + 9 + 13 = 15√157
Therefore, the correct option is (A) 15 √157.
To find the perimeter of the triangle, we need to find the lengths of its sides.
Length of a side of the triangle = magnitude of the difference of the position vectors of its endpoints.
Therefore,
Length of first side = ||(5i 3j-3k) - (i j k)|| = ||4i 2j - 4k|| = 4√6
Length of second side = ||(2i 5j 9k) - (i j k)|| = ||i 4j 8k|| = 9
Length of third side = ||(2i 5j 9k) - (5i 3j-3k)|| = ||-3i 8j 12k|| = 13
Perimeter of the triangle = sum of the lengths of its sides = 4√6 + 9 + 13 = 15√157
Therefore, the correct option is (A) 15 √157.
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Community Answer
If vectors (i+j+k),(5i+3j-3k) and (2i+5j+9k) are the position vectors ...
By using the distance formula we can easily solve this. first write the vertices of the triangle in coordinate form i.e.,(x,y,z) and find the length of each side using distance formula and add all the sides and u r going to get the ans easily .
Distance formula : √(X2-X1)^2+(Y2-Y1)^2+(Z2-Z1)^2
Distance formula : √(X2-X1)^2+(Y2-Y1)^2+(Z2-Z1)^2
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If vectors (i+j+k),(5i+3j-3k) and (2i+5j+9k) are the position vectors of vertices of any triangle then its perimeter isa)15+√157b)15-√157c)√15-√157d)√15+√157Correct answer is option 'A'. Can you explain this answer?
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