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The Vector AB= 3i + 4k and AC = 5i – 2j + 4k are the sides of a triangle ABC. The length of the median through is (A) 18 ½ (B) 72 ½ (C) 33 ½ (D) 288 ½

The Vector AB= 3i + 4k and  AC = 5i – 2j + 4k are the sides of a triangle ABC. The length of the median through is
(A)  18½    (B)  72½    (C)   33½    (D)  288½ 
 

Grade:12th pass

2 Answers

Piyush Kumar Behera
417 Points
6 years ago
A little easy way of approach,
Take A as the origin(0,0)
so Vector AB= 3i + 4k and  AC = 5i – 2j + 4k will become position vector.
So coordinate of B is (3,0,4) and C is(5,-2,4).
The mid point of BC can be easily found by midpoint formula of two points as D(4,-1,4).
so length of median through A is AD=\sqrt{(4-0)^2+(-1-0)^2+(4-0)^2}
                                                           =\sqrt{33}   
So the answer is C.
I have put my best to explain.If you are unable to get please do write I will try to explain again.And please If my answer is correct do approve my answer!!
 
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached solution to your answer.
 
This question would become easy to solve if you notice the similarity between parralelogram law of vector addition and the fact that the diagonal represents the resultant vector and also the diagonals bisects each other.
Let us assume the resultant of vector AC and AB is vector AD. As we know diagonals bisect each other. Hence half of the resultant vector AD will be the median for side BC
Hence, Vector AD = (AC + AB)/2 = (5i – 2j + 4k + 3i + 4k)/2 
                                                 = (8i – 2j + 8k)/2
                                                 = 4i – j + 4k
Hence the length of median = |AD| = (42 + 12 + 42)½
                                                                   = 33½
Hence C) is the correct option.
 
Hope it helps.
Thanks and regards,
Kushagra

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