Home
Class 11
MATHS
If the vectors vec c , vec a=x hat i+y ...

If the vectors ` vec c , vec a=x hat i+y hat j+z hat k and vec b= hat j` are such that ` vec a , vec c and vec b` form a right-handed system, then find ` vec c dot`

Text Solution

Verified by Experts

Since `veca ,vecc and vecb` form a right - handed system,
`vecc = vecb xx veca`
`= hatj xx (xhati + y hatj + z hatk) `
= - x hatk + zhati = z hati - x hatk`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.3|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise single correct answer type|28 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.1|18 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE PUBLICATION|Exercise All Questions|689 Videos

Similar Questions

Explore conceptually related problems

if vec a= 5 hat i -hat j -3 hat k and vec b=hat i+3 hat j - 5 hat k , Find vec a . vec b =?

Find | vec axx vec b| , if vec a= hat i-7 hat j+7 hat k and vec b=3 hat i-2 hat j+2 hat kdot

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

Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i+3 hat j-2 hat k

Find vec axx vec b ,\ if\ vec a=2 hat i+ hat k\ a n d\ vec b= hat i+ hat j+ hat kdot

If vec a= hat i+ hat j+ hat k and vec b= hat i-2 hat j+ hat k , then find vector vec c such that vec a . vec c=2 and vec axx vec c= vec bdot

A vector vec d is equally inclined to three vectors vec a= hat i+ hat j+ hat k , vec b=2 hat i+ hat ja n d vec c=3 hat j-2 hat kdot Let vec x , vec y ,a n d vec z be three vectors in the plane of vec a , vec b ; vec b , vec c ; vec c , vec a , respectively. Then a. vec x. vec d=-1 b. vec y. vec d=1 c. vec z. vec d=0 d. vec r. vec d=0,w h e r e vec r=lambda vec x+mu vec y+delta vec z

Given three vectors vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja n d vec c=-2 hat i+21 hat j such that vecalpha= vec a+ vec b+ vec c Then the resolution of the vector vecalpha into components with respect to vec aa n d vec b is given by a. 3 vec a-2 vec b b. 3 vec b-2 vec a c. 2 vec a-3 vec b d. vec a-2 vec b

If vec a=2 hat i+3 hat j-5 hat k , vec b=m hat i+n hat j+12 hat k and vec axx vec b= vec0, then find (m ,n)dot

If vectors vec A=2 hat i+3 hat j+4 hat k , vec B= hat i+ hat j+5 hat k and vec C form a left-handed system, then vec C is a. 11 hat i-6 hat j- hat k b. -11 hat i+6 hat j+ hat k c. 11 hat i-6 hat j+ hat k d. -11 hat i+6 hat j- hat k