Home
Class 12
MATHS
Find 3-dimensional vectors vec v1,vec v2...

Find 3-dimensional vectors `vec v_1,vec v_2,vec v_3` satisfying `vec v_1* vec v_1=4,vec v_1* vec v_2=-2,vec v_1* vec v_3=6,`
`vec v_2* vec v_2=2 , vec v_2 *vec v_3=-5,vec v_3* vec v_3=29`

A

(a) `vec v_3`=`-3hat(i)+2hat(j)pm4hat(k)`

B

(b) `vec v_3`=`3hat(i)-2hat(j)pm4hat(k)`

C

(c) `vec v_3`=`-2hat(i)+3hat(j)pm4hat(K)`

D

(d) `vec v_3`=`2hat(i)+3hat(j)pm4hat(k)`

Text Solution

Verified by Experts

The correct Answer is:
(b)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|28 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|14 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise For Session 4|7 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

If vec v_1= (2,-3) , vec v_2=(0,1) and vec v_3=(-1,6) , find a unit vector parallel to vec v_1+2 vec v_2-vec v_3 .

Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b vec c]

If vec a , vec ba n d vec c are unit vectors satisfying | vec a- vec b|^2+| vec b- vec c|^2+| vec c- vec a|^2=9, then |2 vec a+5 vec b+5 vec c| is.

For any two vectors vec ua n d vec v prove that ( vec udot vec v)^2+| vec uxx vec v|^2=| vec u|^2| vec v|^2a n d ( vec1+| vec u|^2)( vec1+| vec v|^2)=(1- vec udot vec v)^2+| vec u+ vec v+( vec uxx vec v)|^2

If vec a , vec b , vec c are coplanar vectors, prove that |[vec a, vec b, vec c],[vec a.vec a ,vec a.vec b,vec a.vec c],[vec b.vec a, vec b.vec b, vec b.vec c]|=vec 0 .

Taking vec v_1= hat i+ 2 hat j- hat k , vec v_2= 2 hat i- hat j+ hat k and vec v_3= hat i+ hat j+ hat k verify that (vec v _1*vec v_2 ) vec v_3 != vec v_1(vec v _2* vec v_3) .

Let vec ua n d vec v be unit vectors such that vec uxx vec v+ vec u= vec w and vec wxx vec u= vec vdot Find the value of [ vec u vec v vec w]dot

If vec a and vec b are any two vectors, show that |vec a xxvec b|^2= [[vec a*vec a,vec a*vec b],[vec a*vec b,vec b* vec b]] .

If vec u , vec v and vec w are three non-coplanar vectors, then prove that ( vec u+ vec v- vec w)dot [( vec u- vec v)xx( vec v- vec w)] = vec u dot (vec v xx vec w)

If vec a is perpendicular to vec b and vec r is non-zero vector such that p vec r+( vec rdot vec a) vec b= vec c , then vec r= vec c/p-(( vec adot vec c) vec b)/(p^2) (b) vec a/p-(( vec cdot vec b) vec a)/(p^2) vec a/p-(( vec adot vec b) vec c)/(p^2) (d) vec c/(p^2)-(( vec adot vec c) vec b)/p

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. Let veca=hati+hatj and vecb=2hati-hatk. Then the point of intersection...

    Text Solution

    |

  2. The coordinates of the point P on the line vec r=( hat i+ hat j+ ha...

    Text Solution

    |

  3. Find 3-dimensional vectors vec v1,vec v2,vec v3 satisfying vec v1* ve...

    Text Solution

    |

  4. The position vectors of points a and b are hat(i)-hat(j)+3hat(k) and 3...

    Text Solution

    |

  5. A, B, C and D are four points in space. Using vector methods, prove th...

    Text Solution

    |

  6. Find the value of x Equation is x+2=9

    Text Solution

    |

  7. If the three planes rcdotn1=p1, rcdotn2=p2 and rcdotn3=p3 have a commo...

    Text Solution

    |

  8. A pentagon is formed by cutting a triangular corner from a rectangular...

    Text Solution

    |

  9. In a three-dimensional coordinate system, P ,Q ,a n dR are images o...

    Text Solution

    |

  10. A plane 2x+3y+5z=1 has a point P which is at minimum distance from lin...

    Text Solution

    |

  11. Evaluate int x^5 dx

    Text Solution

    |

  12. A cube C={(x, y, z)|o le x, y, zle1} is cut by a sharp knife along the...

    Text Solution

    |

  13. A ray of light is sent through the point P(1,2,3) and is reflected on ...

    Text Solution

    |

  14. Find dy/dx if 2x-3sinx=2y

    Text Solution

    |

  15. The shortest distance between any two opposite edges of the tetrahedro...

    Text Solution

    |

  16. The angle between the pair of planes represented by equation 2x^(2)-2y...

    Text Solution

    |

  17. Find the value of x Equation is x+1=1

    Text Solution

    |

  18. The four lines drawing from the vertices of any tetrahedron to the cen...

    Text Solution

    |

  19. The shorteast distance from (1, 1, 1) to the line of intersection of t...

    Text Solution

    |

  20. The shortest distance between the two lines L1:x=k1, y=k2 and L2: x=k3...

    Text Solution

    |