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Let veca and vecb are non collinear vect...

Let `veca` and `vecb` are non collinear vectors. If vectors `vecalpha=(lambda-2)veca+vecb` and `vecbeta=(4lambda-2)veca+3vecb` are collinear, then `lambda` is equal to (a) `-4` (b) `4` (c) `2` (d) `-2`

A

4

B

-3

C

3

D

-4

Text Solution

Verified by Experts

The correct Answer is:
D
Two vectors c and d are said to be collinear if we can write c`= lambda b` for some non-zero scalar `lambda`
Let the vectors `a=(lambda -2) a+b`
and `beta= (4lambda -2) a+3b ` are
collinear where a and b are non -collinear
`:. `We can write
`alpha = k beta ` for some `k in R -{0}`
`rArr (lambda-2 ) a+ b = k [(4 lambda -2)a+ 3 b]`
`rArr [(lambda -2) -k (4lambda -2)] a + (1-3k) b=0`
Now as a and b are non- collinear therefore they are linearly independent and hence `(lambda-2) -k (4lambda-2)=0` and `1-3k =0`
`rArr lambda -2 =k (4lambda -2) " and " 3k=1`
`rArr lambda -2 = (1)/(3) (4lambda -2)`
`rArr 3lambda -6 =4 lambda -2`
`rArr lambda =-4`
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