Home
Class 12
MATHS
If vec a=x hat i+2 hat j-\ z hat k and ...

If ` vec a=x hat i+2 hat j-\ z hat k` and ` vec b=3 hat i-\ y hat j+ hat k` are two equal vectors, then write the value of `x+y+zdot`

Text Solution

Verified by Experts

The correct Answer is:
0
`vec(a)=vec(b)rArr(xhat(i)+2hat(j)-zhat(k))-(3hat(i)-yhat(j)+hat(k))`
`rArr x=3, -y=2 and -z=1 rArr x=3, y=-2 and z=-1`
`rArr (x+y+z)=[3+(-2)+(-1)]=0`.
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF THREE VECTORS

    RS AGGARWAL|Exercise Objective Questions|34 Videos

  • PRODUCT OF THREE VECTORS

    RS AGGARWAL|Exercise Exercise 25A|15 Videos

  • PROBABILITY DISTRIBUTION

    RS AGGARWAL|Exercise Exercise 32|32 Videos

  • RELATIONS

    RS AGGARWAL|Exercise Objective Questions|22 Videos

Similar Questions

Explore conceptually related problems

If vec a=xhat i+2hat j-zhat k and vec b=3hat i-yhat j+hat k are two equal vectors,then write the value of x+y+z.

If vec a=xhat i+2hat j-zhat k and vec b=3hat i-yhat j+hat k are two equal vectors,then write the value of x+y+z

Show that If vec(a)=x hat(i)+2hat(j)-z hat(k) and vec(b)=3hat(i)-y hat(j)+hat(k) are two equal vectors, then x+y+z=0 .

Vectors vec A=hat i+hat j-2hat k and vec B=3hat i+3hat j-6hat k are

Let vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i- hat j- hat k be three vectors. A vector vec v in the plane of vec aa n d vec b , whose projection on vec c is 1/(sqrt(3)) is given by a. hat i-3 hat j+3 hat k b. -3 hat i-3 hat j+3 hat k c. 3 hat i- hat j+3 hat k d. hat i+3 hat j-3 hat k

If vec r=x hat i+y hat j+z hat k ,\ then write the value of | vec rxx hat i|^2dot

Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d vec c= hat i+ hat j-2 hat k be three vectors. A vector in the plane of vec ba n d vec c , whose projection on vec a is of magnitude sqrt(2//3) , is a. 2 hat i+3 hat j-3 hat k b. 2 hat i-3 hat j+3 hat k c. -2 hat i- hat j+5 hat k d. 2 hat i+ hat j+5 hat k

If vec A = hat i + 3 hat j + 2 hat K and vec B = 3 hat i + hat j + 2 hat k , then find the vector product vec A xx vec B .

Let vec a = hat i + hat j + hat k, vec b = hat i + 4 hat j - hat k, vec c = hat i + hat j + 2 hat k and hat s be a the unit vector the magnitude of the vector (vec a .vec s)(vec b xx vec c) + (vec b. vec s)(vec c xx vec a) + ( vec c.vec s)(vec a xx vec b) is equal to (A) 1 (B) 2 (C) 3 (D) 4

If vec a=3hat i-2hat j+hat k and vec b=-hat i+hat j+hat k then the unit vector parallel to vec a+vec b, is

RS AGGARWAL-PRODUCT OF THREE VECTORS-Exercise 25B
  1. If vec a=x hat i+2 hat j-\ z hat k and vec b=3 hat i-\ y hat j+ hat ...

    Text Solution

    |

  2. Write a unit vector in the direction of the sum of the vectors vec a=...

    Text Solution

    |

  3. For what value lambda are the vectors vec a=2 hat i+\ lambda hat j...

    Text Solution

    |

  4. Find the value of ' p ' for which the vectors 3 hat i+2 hat j+9 hat k\...

    Text Solution

    |

  5. Find lambda, when the projection of vec a=lambda hat i+ hat j+4 hat k...

    Text Solution

    |

  6. If vec(a) and vec(b) are perpendicular vectors such that |vec(a)+vec(b...

    Text Solution

    |

  7. Find | vec x| , if for a unit vector vec a ,\ ( vec x- vec a)dot( vec...

    Text Solution

    |

  8. Find the sum of the vectors vec(a)=(hat(i)-3hat(k)), vec(b)=(2hat(j)-h...

    Text Solution

    |

  9. Find the sum of the following vectors vec a= hat i-2 hat j ,\ vec b=...

    Text Solution

    |

  10. Writhe the projection of the vector 7 hat i+ hat j-4 hat k on the vect...

    Text Solution

    |

  11. Find [vec(a)vec(b)vec(c)], when (i) vec(a)=2hat(i)+hat(j)+3hat(k), v...

    Text Solution

    |

  12. Find [vec(a)vec(b)vec(c)], when (i) vec(a)=2hat(i)+hat(j)+3hat(k), v...

    Text Solution

    |

  13. Find a vector in the direction of vector 2 hat i-3 hat j+6 hat k which...

    Text Solution

    |

  14. If veca=2hati+2hatj+3hatk, vecb=-hati+2hatj+hatk and vecc=3hati+hatj t...

    Text Solution

    |

  15. Write a vector of magnitude 15 units in the direction of vecor (hat(i...

    Text Solution

    |

  16. If vec a= hat i+ hat j+ hat k , vec b=4 hat i-2 hat j+3 hat k and ve...

    Text Solution

    |

  17. Write the projection of the vector hat i- hat j on the vector ha...

    Text Solution

    |

  18. Writhe the angle between two vectors vec a\ a n d\ vec b"\ " with ma...

    Text Solution

    |

  19. Find | vec axx vec b| , if vec a= hat i-7 hat j+7 hat ka n d vec b=3 ...

    Text Solution

    |

  20. Find the angle between two vectors vec(a) and vec(b) with magnitudes 1...

    Text Solution

    |