The vectors AB = 3i + 5j + 4k and AC = 5i − 5j + 2k are side of a Δ ABC. The length of the median through A is

Question

The vectors AB = 3i + 5j + 4k and AC = 5i − 5j + 2k are side of a Δ ABC. The length of the median through A is (A) √13 units (B) 2√5 units (C) 5 units (D) 10 units

Tardigrade Admin · Accepted Answer

Position vector of AD =((3+5) i +(5-5) j +(4+2) k /2) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/63bab98f066f491fe84441e48e15e145-.png" /> A D =(8 i +6 k /2)=4 i +3 k ∴ Length of median =| A D | =√16+9=5 units

Q. The vectors $A B = 3 i + 5 j + 4 k$ and $A C = 5 i - 5 j + 2 k$ are side of a $Δ A BC$ . The length of the median through $A$ is

$13$ units

$25$ units

$5$ units

$10$ units

Position vector of AD
$= \frac{( 3 + 5 ) i + ( 5 - 5 ) j + ( 4 + 2 ) k}{2}$

$A D = \frac{8 i + 6 k}{2} = 4 i + 3 k$
$∴$ Length of median $= ∣ A D ∣$
$= 16 + 9 = 5$ units

Q. The vectors AB=3i+5j+4k and AC=5i−5j+2k are side of a ΔABC. The length of the median through A is

13​ units

25​ units

5 units

10 units