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if the vectors a=3i+j-2k,b=-i+3j+4k,c=4i-2j-6k costitiute sides of a triangle ABC then the length of median bisecting vector c is

if the vectors a=3i+j-2k,b=-i+3j+4k,c=4i-2j-6k costitiute sides of a triangle ABC then the length of median bisecting vector c is
 

Grade:11

2 Answers

Vikas TU
14149 Points
4 years ago
Let CC1 be the median 
CC1 = |CC1| = |1/2 (CA + CB)|
|1/2 (a-c+b-c)| = |1/2(a+b-2c)|
|1/2(3i +j -2k-i+3j+4k-2(4i-2j-6k)|
=|-3i+4j+7k| = sqrt(9+16+49)
=> sqrt(74)
Hope this helps 
Aditya Gupta
2081 Points
4 years ago
as usual, vikas’ answer is wrong.
note that for any triangle ABC, AB + BC + CA= 0 where bold chars represent vectors.
now, if here we let a= BC= 3i + j – 2k, b= AC= – CA= –i + 3j + 4k then c= 4i – 2j – 6k= BC+CA= – AB= BA
so now median length bisecting c is= |b + (c/2)|
= |i + 2j + k|
= sqrt(1+4+1)
= sqrt(6)
kindly approve :=)

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