Home
Class 12
MATHS
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)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the area of the triangle formed by the tips of the vectors vec(a) = hati - hatj - 3hatk, vec(b) = 4hati - 3hatj +hatk and vec(c) = 3 hati - hatj +2 hatk .

Show that the vectors vec(a)=hati-2hatj+3hatk,vec(b)=-2hati+3hatj-4hatk and vec( c )=hati-hatj+5hatk are coplannar.

The position vectors of the points A, B, C are 2 hati + hatj - hatk , 3 hati - 2 hatj + hatk and hati + 4hatj - 3 hatk respectively . These points

Find [vec(a)vec(b)vec( c )] if vec(a)=hati-2hatj+3hatk,vec(b)=2hati-3hatj+hatk and vec( c )=3hati+hatj-2hatk .

Show that the vectors, vec(a)=hati-2hatj+3hatk,vec(b)=-2hati+3hatj-4hatk and vec( c )=hati-3hatj+5hatk are coplanar.

Find |vec(a)xx vec(b)| , if vec(a)=hati-7hatj+7hatk and vec(b)=3hati-2hatj+2hatk .

If vecA 2 hati +hatj -hatk, vecB=hati +2hatj +3hatk, vecC=6hati -2hatj-6hatk angle between (vecA+vecB) and vecC will be

vec(a)=2hati-10hatj+2hatk,vec(b)=3hati+hatj+2hatk and vec( c )=2hati+hatj+3hatk then find vec(a)xx(vec(b)xxvec( c )) .