Home
Class 12
MATHS
Find the value of lambda for which the t...

Find the value of `lambda` for which the three points with position vector `3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k , and4 hat i+5 hat j+lambda hat k` are coplanar.

Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

Similar Questions

Explore conceptually related problems

find the projection of 3hat i - hat j + 4hat k on 2 hat i + 3 hat j -6 hat k

Find the value of lambda if the volume of a tetrahedron whose vertices are with position vectors hat i-6 hat j+10 hat k ,- hat i-3 hat j+7 hat k ,5 hat i- hat j+lambda hat k and 7 hat i-4 hat j+7 hat k is 11 cubic unit.

Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k and 2 hat i + 5 hat j - hat k from a triangle in space.

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

Find the area of triangle whose vertices have position vectors hat (i) + hat (j) + 2 hat (k) , 2 hat (i) + 2 hat (j) + 3 hat (k) and 3 hat (i) - hat (j) - hat (k)

Find the value of lamda if three vectors vec(a) = 2hat(i) - hat(j) + hat(k), vec(b) = hat(i) + 2hat(j) - 3hat(k) and vec(c) = 3hat(i) + lamda hat(j) + 5hat(k) are coplanar

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot

Find the projection of vector hat i+3 hat j+7 hat k on the vector 7 hat i- hat j+8 hat kdot

The position vectors of the point A ,B ,C and D are 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k ,- hat i+ hat j+2 hat k and 4 hat i+5 hat j+lambda hat k , respectively. If the points A ,B ,C and D lie on a plane, find the value of lambda .

Prove that the four points 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k and 2 hat i+5 hat j+10 hatk form a tetrahedron in space.

CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Solve sin^(-1)((14)/(|x|))+sin^(-1)((2sqrt(15))/(|x|))=pi/2

    Text Solution

    |

  2. Find the minimum value of (sec^(-1)x)^2+("c o s e c"^(-1)x)^2

    Text Solution

    |

  3. Find the value of lambda for which the three points with position vect...

    Text Solution

    |

  4. Solve sin^(-1)xlt=cos^(-1)xdot

    Text Solution

    |

  5. If 3tan^(-1)(1/(2+sqrt(3)))-tan^(-1)(1/x)=tan^(-1)(1/3), then x is equ...

    Text Solution

    |

  6. The value 2tan^(-1)[sqrt((a-b)/(a+b))tan(theta/2)] is equal to cos^(-1...

    Text Solution

    |

  7. If 1/2sin^(-1)[(3sin2theta)/(5+4cos2theta)]=tan^(-1)x ,t h e nx= (a...

    Text Solution

    |

  8. If cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x , then sinx is ...

    Text Solution

    |

  9. The value of tan^(-1)((xcostheta)/(1-xsintheta))-cot^(-1)((costheta)/(...

    Text Solution

    |

  10. tan(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(-1)x),x!=0, is equal to x (b)...

    Text Solution

    |

  11. The sum of series sec^(-1) sqrt2 + sec^(-1).(sqrt10)/(3) + sec^(-1).(s...

    Text Solution

    |

  12. The value of tan^(-1).(4)/(7) + tan^(-1).(4)/(19) + tan^(-1).(4)/(39) ...

    Text Solution

    |

  13. If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(...

    Text Solution

    |

  14. If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x ...

    Text Solution

    |

  15. If alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^4)),beta=2sin^(-1)((2x)/(1+x^2))...

    Text Solution

    |

  16. Absolute value of sum of all integers in the domain of f(x)=cot^(-1)sq...

    Text Solution

    |

  17. Solve the equation tan^(-1)2x+tan^(-1)3x=pi/4

    Text Solution

    |

  18. Solve tan^(-1)x+sin^(-1)x=tan^(-1)2xdot

    Text Solution

    |

  19. 2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),where x in R-{-1,1}, is equal to

    Text Solution

    |

  20. If alpha=3sin^-1(6/(11)) and beta=3cos^-1(4/9), where the inverse trig...

    Text Solution

    |