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Let A(3,0,-1) ,B(2,10,6) and C(1,2,1) be...

Let A(3,0,-1) ,B(2,10,6) and C(1,2,1) be the vertices of a triangle and M be the mid- point of AC.
If G divides BM in the ratio `2:1` then cos `( angle GOA)` (O being the origin) is equal to

A

`1/(2sqrt(15))`

B

`1/sqrt(30)`

C

`1/sqrt(15)`

D

`1/(6sqrt(10))`

Text Solution

Verified by Experts

The correct Answer is:
C
M be the mid point of AC
So, `M-=(2,1,0)`
According to the information given in the question G be the centroid of the triangle.
G=(2,4,2)
Now, `bar(O)A=3hati -hatk`
`barOG' = 2hati + 4hati + 2hatk`
`cos(angleGOA) =(6-2)/(sqrt(10)sqrt(4+16+4))`
`cos(angleGOA)=4/sqrt(240) = 1/sqrt(15)`
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