When $\vec A \cdot \vec B = - |A||B|$,then

  • A
    $\vec A$ and $\vec B$ are perpendicular to each other
  • B
    $\vec A$ and $\vec B$ act in the same direction
  • C
    $\vec A$ and $\vec B$ act in the opposite direction
  • D
    $\vec A$ and $\vec B$ can act in any direction

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Explain position and displacement vectors. How is the magnitude of a vector quantity represented?

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$(a) \quad |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}|$
$(b) \quad |\vec{a} + \vec{b}| \geq ||\vec{a}| - |\vec{b}||$
$(c) \quad |\vec{a} - \vec{b}| \leq |\vec{a}| + |\vec{b}|$
$(d) \quad |\vec{a} - \vec{b}| \geq ||\vec{a}| - |\vec{b}||$
When does the equality sign apply in each case?

Given two vectors $\vec{A}$ and $\vec{B}$,such that $\vec{A} + \vec{B} = \vec{C}$ and $A^2 + B^2 = C^2$. Which of the following statements is true?

If $|\vec{v}_1 + \vec{v}_2| = |\vec{v}_1 - \vec{v}_2|$ and $\vec{v}_1$ and $\vec{v}_2$ are finite,then:

If the angle between $\hat{a}$ and $\hat{b}$ is $60^{\circ}$,then which of the following vector$(s)$ have magnitude one?

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