(A) Let $A$ be the origin $(0, 0, 0)$.Then the coordinates of $B$ are $(3, 0, 4)$ and the coordinates of $C$ are $(5, -2, 4)$.The median through $A$ m

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(A) Let $A$ be the origin $(0, 0, 0)$.Then the coordinates of $B$ are $(3, 0, 4)$ and the coordinates of $C$ are $(5, -2, 4)$.The median through $A$ meets the side $BC$ at its midpoint $M$.The coordinates of the midpoint $M$ of $BC$ are given by $\left( \frac{3+5}{2}, \frac{0-2}{2}, \frac{4+4}{2} \right) = (4, -1, 4)$.The length of the median $AM$ is the distance from $A(0, 0, 0)$ to $M(4, -1, 4)$.Length $= \sqrt{(4-0)^2 + (-1-0)^2 + (4-0)^2} = \sqrt{16 + 1 + 16} = \sqrt{33} \text{ units}$.

Class 12 Mathematics Vector Algebra Basic , Modulus and Algebra of vectors

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The vectors $\overrightarrow{AB} = 3 \hat{i} + 4 \hat{k}$ and $\overrightarrow{AC} = 5 \hat{i} - 2 \hat{j} + 4 \hat{k}$ are the sides of a triangle $ABC$. The length of the median through $A$ is

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A
$\sqrt{33} \text{ units}$
B
$\sqrt{288} \text{ units}$
C
$\sqrt{18} \text{ units}$
D
$\sqrt{72} \text{ units}$

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The vectors $\overrightarrow{AB} = 3 \hat{i} + 4 \hat{k}$ and $\overrightarrow{AC} = 5 \hat{i} - 2 \hat{j} + 4 \hat{k}$ are the sides of a triangle $ABC$. The length of the median through $A$ is

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