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Number of integral value(s) of lambda fo...

Number of integral value(s) of `lambda` for which vectors `x^(2)hati-hatj+xhatk, (lambda-1)hati-2lambdahatj+hatk` and `hati-hatj+hatk`, in the order from right-handed system `AA x` `in`R, is

A

0

B

2

C

4

D

6

Text Solution

Verified by Experts

The correct Answer is:
A
`|{:(x^(2),-1,x),(lambda-1,-2lambda,1),(1,-1,1):}| gt 0`
`(2lambda-1)x^(2)-(lambda+1)x-(lambda-2) lt 0 AA x in R`
`2lambda-1 gt 0` and `(lambda+1)^(2)+4(2lambda-1)(lambda-2) gt 0`
`rArr lambda^(2)-2lambda+1 gt 0` and `lambda gt 1/2`
`rArr (lambda-1)^(2)` and `lambda gt 1/2`
`rArr` there is no value of `lambda`.
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Knowledge Check

  • The value of lambda for which the vectors 3hati-6hatj+hatk and 2hati-4hatj+lambdahatk are parallel is

    A
    `(2)/(3)`
    B
    `(3)/(2)`
    C
    `(5)/(2)`
    D
    `(2)/(5)`

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