Home
Class 12
MATHS
let veca , vecb and vecc be three vector...

let `veca , vecb and vecc` be three vectors having magnitudes 1, 1 and 2, respectively, if `vecaxx(vecaxxvecc)+vecb=vec0, ` then the acute angle between `veca and vecc` is _______

Text Solution

Verified by Experts

The correct Answer is:
`pi//6`
`veca xx (vecaxxvecc) +vecb=vec0`
`or (veca.vecc)veca-(veca.veca)vecc+vecb=vec0`
`or 2 cos theta. veca-vecc+vecb=vec0`
(using `|veca|=1,|vecb|=1,|vecc|=2`)
`or (2costheta veca-vecc)^(2)=(-vecb)^(2)`
`or 4cos^(2)theta.|veca|^(2)+|vecc|^(2)`
`-2.2 cos theta.veca.vecc=|vecb|^(2)`
`or 4cos^(2)theta+4-8costheta.costheta=1`
`or cos^(2)theta-8cos^(2)theta+4=1`
`or 4 cos^(2) theta=3`
`or cos theta = +- sqrt3//2`
for `theta` to be acute , `cos theta= sqrt3/2 Rightarrow theta= pi/6`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise True and false|3 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 Subjective type|19 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

Similar Questions

Explore conceptually related problems

If veca+vecb=vecc , and a+b=c then the angle between veca and vecb is

veca,vecb and vecc are three orthogonal vectors with magnitudes 3, 4 and 12 respectively. The value of abs(veca+vecb+vecc) =

If veca+vecb=vecc and a+b=c , find the angle between veca and vecb .

Let veca, vecb and vecc be the three vectors having magnitudes, 1,5 and 3, respectively, such that the angle between veca and vecb "is " theta and veca xx (veca xxvecb)=vecc . Then tan theta is equal to

veca+vecb+vecc=vec0, |veca|=3, |vecb|=5,|vecc|=9 ,find the angle between veca and vecc .

Let veca,vecb and vecc be the non zero vectors such that (vecaxxvecb)xxvecc=1/3 |vecb||vecc|veca. if theta is the acute angle between the vectors vecb and vecc then sintheta equals (A) 1/3 (B) sqrt(2)/3 (C) 2/3 (D) 2sqrt(2)/3

If three unit vectors veca, vecb and vecc " satisfy" veca+vecb+vecc= vec0 . Then find the angle between veca and vecc .

If veca +vecb +vecc=0, |veca|=3,|vecb|=5, |vecc|=7 , then find the angle between vecb and vecc .

If three unit vectors veca, vecb and vecc " satisfy" veca+vecb+vecc= vec0 . Then find the angle between vecb and vecc .