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If vector hat(i)+hat(j)+hat(k), hat(i)-h...

If vector `hat(i)+hat(j)+hat(k), hat(i)-hat(j)+hat(k)` and `2hat(i)+3hat(j)+lambda hat(k)` are coplanar, then `lambda` is equal to

A

`-2`

B

3

C

2

D

`-3`

Text Solution

Verified by Experts

The correct Answer is:
C
Since, vectors `hati+hatj+hatk, hati-hatj+hatk" and "2hati+3hatj+lamdahatk` are coplanar, therefore
`|{:(1,1,1),(1,-1,1),(2,3,lamda):}|=0`
`rArr" "2(-lamda-3)-1(lamda-2)+1(3+2)=0`
`rArr" "-lamda-3 -lamda+2+5=0`
`rArr" "2lamda=4lamda=2`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-VECTORS -( MHT CET Corner)
  1. The position vectors of vertices of a Delta ABC are 4hat(i)-2hat(j), h...

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  2. Given p=3hat(i)+2hat(j)+4hat(k), a=hat(i)+hat(j), b=hat(j)+hat(k), c=h...

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  3. Volume of the parallelopiped having vertices at O equiv (0, 0, 0), A e...

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  4. If 2a+3b-5c=0, then ratio in which c divides AB is

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  5. If the constant due to which it is displaced from a point on a particl...

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  6. If the vectors hat(i)-3hat(j)+2hat(k), -hat(i)+2hat(j) represent the d...

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  7. If |a|=2, |b|=3 and a, b are mutually perpendicular, then the area of ...

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  8. a xx [axx(axxb)] is equal to

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  9. If the vectors a+ lambda b+3c, -2a+3b-4c and a-3b+5c are coplanar, the...

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  10. If the vectors a=hat(i)+a hat(j)+a^(2) hat(k), b=hat(i)+b hat(j)+b^(2)...

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  11. Let a=2hat(i)-hat(j)+hat(k), b=hat(i)+2hat(j)-hat(k) and c=hat(i)+hat(...

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  12. (a.(b xx c))/(b.(c xx a))+(b.(a x b))/(a. (b xx c)) is equal to

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  13. If |a|=|b|=1 and |a+b|=sqrt(3), then the value of (3a-4b).(2a+5b) is

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  14. If a is perpendicular to b and c, |a|=2, |b|=3, |c|=4 and the angle be...

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  15. If a, b and c are perpendicular to b+c, c+a and a+b respectively and i...

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  16. If vector hat(i)+hat(j)+hat(k), hat(i)-hat(j)+hat(k) and 2hat(i)+3hat(...

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  17. Given a bot b, |a|=1 and if (a+3b).(2a-b)=-10, then |b| is equal to

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  18. [(a+b,b+c,c+a)]=[(a,b,c)], then

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  19. Area of rhombus is ......., where diagonals are a=2hat(i)-3hat(j)+5hat...

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  20. Let ABCD be a parallelogram whose diagonals intersect at P and O be th...

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