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If theta is the angle between any two v...

If `theta` is the angle between any two vectors ` veca` and ` vec b`, then `| veca . vecb |=| veca xx vecb|` when `theta` is equal to(A) 0 (B) `pi/4` (C) `pi/2` (D) `pi`

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To solve the problem, we need to find the angle \( \theta \) between two vectors \( \vec{a} \) and \( \vec{b} \) such that the magnitude of their dot product is equal to the magnitude of their cross product. ### Step-by-step Solution: 1. **Write the expressions for dot product and cross product:** - The dot product of two vectors is given by: \[ |\vec{a} \cdot \vec{b}| = |\vec{a}| |\vec{b}| \cos \theta ...
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Knowledge Check

  • If theta is the angle between unit vectors vecA and vecB , then ((1-vecA.vecB))/(1+vecA.vecB)) is equal to

    A
    `tan^(2)(theta//2)`
    B
    `sin^(2)(theta//2)`
    C
    `cot^(2)(theta//2)`
    D
    `cos^(2)(theta//2)`
  • Angle between the vectors sqrt3(veca xx vec b) " and " vec b - (veca .vecb)veca is

    A
    `pi/2`
    B
    0
    C
    `pi/4`
    D
    `pi/3`
  • The angle between the vectors vecA and vecB is theta. The value of vecA(vecAxx vec B) is -

    A
    `A^(2)B`
    B
    zero
    C
    `A^(2)B sin theta`
    D
    `A^(2)B cos theta`
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