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Write all the unit vectors in XY-plane....

Write all the unit vectors in XY-plane.

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Knowledge Check

  • Let vec(u)=2hat(i)-hat(j)+hat(k) and vec(v)=-3hat(j)+2hat(k) be vectors in R^(3) and vec(w) be a unit vector in the xy-plane . Then the maximum possible value of |(vec(u)xxvec(v))*vec(w)| is

    A
    `5`
    B
    `12`
    C
    `13`
    D
    `17`

  • Let vec(u)=2hat(i)-hat(j)+hat(k),vec(v)=-3hat(j)+2hat(k) be vectors and vec(w) be a unit vector in the xy-plane . Then the maximum possible value of |(vec(u)xxvec(v))*vec(w)| is

    A
    `sqrt(5)`
    B
    `sqrt(12)`
    C
    `sqrt(13)`
    D
    `sqrt(17)`

  • 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)))`

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