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If veca and vecb are unit vectors inclin...

If `veca` and `vecb` are unit vectors inclined at an angle `theta`,then prove that `sin(theta/2)=1/2|veca-vecb| `

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Knowledge Check

  • If veca, vecb and vecc are three unit vectors equally inclined to each other at an angle alpha . Then the angle between veca and plane of vecb and vecc is

    A
    `theta =cos^(-1)((cos alpha)/("cos"(alpha)/(2)))`
    B
    `theta =sin^(-1)((cos alpha)/("cos"(alpha)/(2)))`
    C
    `theta =sin^(-1)((cos alpha)/("cos"(alpha)/(2)))`
    D
    `theta =cos^(-1)((sin alpha)/("sin"(alpha)/(2)))`

  • Let 'veca' and 'vecb' be two unit vectors and 'theta' is the angle between them. Then 'veca,+vecb' is a unit vector if

    A
    theta=pi/4'
    B
    theta=pi/3'
    C
    theta=pi/2'
    D
    theta=2 fra.pi/3'

  • If veca and vecb are two non collinear unit vectors and if |veca+vecb|=sqrt(3) then the valueof (veca-vecb).(2veca+vecb)

    A
    `1/(sqrt(2))`
    B
    `1/(sqrt(3))`
    C
    `1/2`
    D
    `1/3`

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    For any three vectors veca,vecb and vecc , and, prove that (veca+vecb)+vecc=veca+(vecb+vecc) .

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    Two.vectors vecA and vecB are inclined at an angle theta . Now if the vectors are interchanged, then the resultant through an angle alpha . Which of the following relation is true? .

    Two vectors vecA and vecB are inclined to each other at an angle theta . Which of the following is the unit vector perpendicular to both vecA and vecB ?

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