Find the magnitude of the vector which joins the point $A$ $(- 1, - 3, - 1)$ to $B$ $(0, 0, 0)$ .

\sqrt{21}

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\sqrt{10}

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\sqrt{11}

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None of these

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Solution

The correct option is C $\sqrt{11}$
Given points
$A (- 1, - 3, - 1)$ and $B (0, 0, 0)$
$\to O A = -^i - 3^j -^k$
$\to O B = 0$
vector AB from A to B
$\to A B = \to O B - \to O A$
$\to A B = 0 - (-^i - 3^j -^k)$
$\to A B = +^i + 3^j +^k)$
magnitude of AB
$∣ ∣ \to A B ∣ ∣ = \sqrt{1^{2} + 3^{2} + 1^{2}}$

$∣ ∣ \to A B ∣ ∣ = \sqrt{1 + 9 + 1}$

$∣ ∣ \to A B ∣ ∣ = \sqrt{11}$

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