Two non-zero vectors A- and B- are drawn from a common point and vecC - A- - B- then which of the option incorrect regarding the angle between A- and B-

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Standard XII

Physics

Vectors and Its Types

Two non-zero ...

Question

Two non-zero vectors $\to A$ and $\to B$ are drawn from a common point and $v e c C = \to A + \to B$ , then which of the option incorrect regarding the angle between $\to A$ and $\to B$

90^{o}

C^{2} = A^{2} + B^{2}

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Greater than

90^{o}

C^{2} < A^{2} + B^{2}

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Greater than

90^{o}

C^{2} > A^{2} + B^{2}

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Less than

90^{o}

C^{2} > A^{2} + B^{2}

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Solution

The correct option is C Greater than $90^{o}$ if $C^{2} > A^{2} + B^{2}$
$C^{2} = A^{2} + B^{2} + 2 A B cos θ$
If $θ = 90^{0}$
$C^{2} = A^{2} + B^{2}$
If $θ > 90^{0}$
$\begin{matrix} C^{2} = A^{2} + B^{2} + 2 A B ∴ C^{2} < A^{2} + B^{2} \end{matrix}$
$∴$ Option $C$ is incorrect.

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Two non-zero vectors →A and →B are drawn from a common point and vecC=→A+→B, then which of the option incorrect regarding the angle between →A and →B

The correct option is C Greater than 90o if C2>A2+B2C2=A2+B2+2ABcosθIf θ=900C2=A2+B2If θ>900C2=A2+B2+2AB∴C2<A2+B2∴ Option C is incorrect.

Two non-zero vectors $\to A$ and $\to B$ are drawn from a common point and $v e c C = \to A + \to B$ , then which of the option incorrect regarding the angle between $\to A$ and $\to B$

The correct option is C Greater than $90^{o}$ if $C^{2} > A^{2} + B^{2}$
$C^{2} = A^{2} + B^{2} + 2 A B cos θ$
If $θ = 90^{0}$
$C^{2} = A^{2} + B^{2}$
If $θ > 90^{0}$
$\begin{matrix} C^{2} = A^{2} + B^{2} + 2 A B ∴ C^{2} < A^{2} + B^{2} \end{matrix}$
$∴$ Option $C$ is incorrect.