Find the magnitude of the vector which joins the point $A$ $(4, 5, 6)$ to $B$ $(10, 11, 12)$ .

12.29

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10.39

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10.29

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None of these

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Solution

The correct option is B $10.39$
Given points
$A (4, 5, 6)$ and $B (10, 11, 12)$
$\to O A = 4^i + 5^j + 6^k$
$\to O B = 10^i + 11^j + 12^k$
vector
$\to A B = \to O B - \to O A$
$\to A B = 10^i + 11^j + 12^k - (4^i + 5^j + 6^k)$
$\to A B = 10^i + 11^j + 12^k - 4^i - 5^j - 6^k$
$\to A B = 6^i + 6^j + 6^k$
magnitude of AB
$∣ ∣ \to A B ∣ ∣ = \sqrt{6^{2} + 6^{2} + 6^{2}}$

$∣ ∣ \to A B ∣ ∣ = \sqrt{36 + 36 + 36}$

$∣ ∣ \to A B ∣ ∣ = \sqrt{36 \times 3}$

$∣ ∣ \to A B ∣ ∣ = 6 \sqrt{3}$

$∣ ∣ \to A B ∣ ∣ = 6 \times 1.732$

$∣ ∣ \to A B ∣ ∣ = 10.39$

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Find the magnitude of the vector which joins the point A(4,5,6) to B(10,11,12).

Find the magnitude of the vector which joins the point $A$ $(4, 5, 6)$ to $B$ $(10, 11, 12)$ .