Home
Class 12
MATHS
Consider the set of eight vector V={a ha...

Consider the set of eight vector `V={a hat i+b hat j+c hat k ; a ,bc in {-1,1}}dot` Three non-coplanar vectors can be chosen from `V` is `2^p` ways. Then `p` is_______.

Text Solution

Verified by Experts

The correct Answer is:
5
Let `(1, 1, 1), (-1, 1, 1),(1, -1, 1),(-1, -1, 1)` be vectors `veca, vecb, vecc, vecd`, rest of the vectors are `-veca, -vecb, -vecc, -vecd ` and let us find the number of ways of selecting coplanar vectors.
Observe that out of any three coplanar vecors two will be collinear (anti parallel).
Number of ways of selecting the anti-parallel pair =4
Number of ways of selecting the third vector =6
Total = 24
Number of non-coplanar selections
`" " = ""^(8)C_(3)- 24 = 32 = 2^(5), p=5`
`therefore p =5`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise ARCHIVES SUBJECTIVE TYPE|9 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise FILL IN THE BLANKS|2 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise MATRIX-MATCH TYPE|3 Videos

  • INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|762 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|541 Videos

Similar Questions

Explore conceptually related problems

Consider th set of eight vectors V = {a hat(i) + b hat(j) + c hat(k): a, b, c in {-1, 1}} . Three non-coplanar vectors can be chosen from V in 2P ways Then p is

Consider the set of eight vectors V[ahati+bhatj+chatk:a,b,c in {1-1}] . Three non-coplanar vectors cann be chosen from V in 2^(p) ways, then p is

Find the unit vector in the direction of the vector vec a= hat i+ hat j+ 2 hat k .

If the vector ahat i+ a hat j+ c hatk, hat i+hatk and chat i+c hat j+b hat k be coplanar, show that c^2= ab .

Find the angle between the vectors vec a= hat i+hat j-hat k and vec b=hat i-hat j+hat k

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

For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .

Find the resultant of vectors vec a= hat i- hat j+2 hat k and vec b= hat i+2 hat j-4 hat kdot Find the unit vector in the direction of the resultant vector.

Statement 1: A component of vector vec b=4 hat i+2 hat j+3 hat k in the direction perpendicular to the direction of vector vec a= hat i+ hat j+ hat ki s hat i- hat jdot Statement 2: A component of vector in the direction of vec a= hat i+ hat j+ hat k is 2 hat i+2 hat j+2 hat kdot

Find the vector of length 3 unit which is perpendicular to hat i+ hat j+ hat k and lies in the plane of hat i+ hat j+ hat k and 2 hat i-3 hat j .