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The number of distinct real values of `lambda` , for which the vectors `-lambda^2 hat i+ hat j+k , hat i-lambda^2 hat j+ hat ka n d hat i+ hat j-lambda^2 hat k` are coplanar is a. zero b. one c. two d. three

A

`0`

B

`1`

C

`pmsqrt(2)`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let two non-collinear unit vectors veca and vecb form an acute angle. ...

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  2. Let the vectors PQ,OR,RS,ST,TU and UP represent the sides of a regular...

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  3. The number of distinct real values of lambda , for which the vectors...

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  4. Let veca,vecb,vecc be unit vectors such that veca+vecb+vecc=vec0. Whic...

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  5. Let vec A be a vector parallel to the line of intersection of plan...

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  6. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

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  7. The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk an...

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  8. The value of a so that the volume of parallelepiped formed by hat i...

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  9. If vec a=( hat i+ hat j+ hat k), vec a. vec b=1a n d vec axx vec b= h...

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  10. Let vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...

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  11. If veca and vecb are two unit vectors such that veca + 2vecb and 5 vec...

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  12. Let a= 2hat(i) -2hat(k) , b=hat(i) +hat(j) and c be a vectors suc...

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  13. If [axxb bxxc c xxa]=lambda[abc]^(2), then lambda is equal to

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  14. Let hata and hatb be two unit vectors. If the vectors vecc=hata+2hatb ...

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  15. Let ABCD be a parallelogram such that vec A B= vec q , vec A D= vec p...

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  16. veca =1/sqrt(10)(3hati + hatk) and vecb =1/7(2hati +3hatj-6hatk), then...

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  17. The vectors vec a and vec b are not perpendicular and vec c and v...

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

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  19. Let veca =hatj-hatk and vecc =hati-hatj-hatk. Then the vector b satisf...

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  20. If the vectors veca=hati-hatj+2hatk.vecb=2hati+4hatj+hatk and veccc=la...

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