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If the vectors ahat(i)+hat(j)+hat(k), ha...

If the vectors `ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+hat(j)+chat(k), (anebnec)` are coplanar, then `(1)/(1-a)+(1)/(1-b)+(1)/(1-c)=`

A

0

B

1

C

-1

D

2

Text Solution

Verified by Experts

The correct Answer is:
A, C
`I=underset(1)overset(2)(int)(e^(x))/(x)dx`
`f(x)=(e^(x))/(x),f'(x)=((x-1)e^(x))/(x^(2))gt 0 [AA x in (1,2)]`
`rarrIgtAr.[ACDE]`
` I gt e xx 1 implies I gt e ....(1)`
`rarr I lt "Area of trapezium ABCDE"`
`Ilt (1)/(2)(1)[e+(e^(2))/(2)]`
`I lt (e)/(2)+(e^(2))/(4)" ".......(2)`
`(I gt 3+(e)/(2))` is false from (2)
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Knowledge Check

  • If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+hat(j)+chat(k) , where a, b, c are coplanar, then a+b+c-abc=

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