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A,B C and dD are four points such that v...

A,B C and dD are four points such that `vec (AB) = m(2 hati - 6 hatj + 2hatk) vec(BC) = (hati - 2hatj) and vec(CD) = n (-6 hati + 15 hatj - 3 hatk)`. If CD intersects AB at some points E, then

A

`m ge(1)/(2)`

B

`nge(1)/(3)`

C

`m=n`

D

`m lt n`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Let EB=p AB and CE =qCD
Then `0 lt p and q le1`

Since, EB+BC+CE=0
`p m(2hati-6hatj+2hatk)+(2hati-2hatj)+qn(-6hati+15hatj-3hatk)=0`
`implies(2p m+1-6qn)hati+(-6p m-2+15qn)hatj+(2p m-6qn)hatk=0`
`implies2p m-6qn+1=0`,
`-6p m-2+15qn=0`
`2 p m-6qn=0`
Solving these, we get
`p=(1)/((2m)) and q=(1)/((3n))`
`therefore 0 lt (1)/((2m)) le 1 and 0 lt (1)/((3n)) le 1`
`implies m ge (1)/(2) and n ge (1)/(3)`
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