The two vectors hati + hatj + hatk and hati +3 hatj +5 hatk represent the two sides overlineAB and overlineAC respectively of a ΔABC. The length of the median through A is

Question

The two vectors hati + hatj + hatk and hati +3 hatj +5 hatk represent the two sides overlineAB and overlineAC respectively of a ΔABC. The length of the median through A is (A) (√14/2) (B) 14 (C) 7 (D) √14

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/chemistry/21a099f06081247b6d5f970c007c27d2-.png" /> A B=(1,1,1), A C=(1,3,5) ⇒ B C=A C-A B=(0,2,4) Since D is the mid-point of B C, ∴ B D=(0,1,2) A D=A B+B D =(1,2,3) ∴ |A D| =√1+4+9 =√14

Q. The two vectors $\hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + 3 \hat{j} + 5 \hat{k}$ represent the two sides $\overline{A B}$ and $\overline{A C}$ respectively of a $Δ$ ABC. The length of the median through A is

$\frac{14}{2}$

$14$

$7$

$14$

$A B = (1, 1, 1), A C = (1, 3, 5)$
$\Rightarrow BC = A C - A B = (0, 2, 4)$
Since $D$ is the mid-point of $BC$ ,
$∴ B D = (0, 1, 2)$
$A D = A B + B D$
$= (1, 2, 3)$
$∴ ∣ A D ∣ = 1 + 4 + 9$
$= 14$

Q. The two vectors i^+j^​+k^ and i^+3j^​+5k^ represent the two sides AB and AC respectively of a ΔABC. The length of the median through A is

214​​

14

7

14​

AB=(1,1,1),AC=(1,3,5) ⇒BC=AC−AB=(0,2,4) Since D is the mid-point of BC, ∴BD=(0,1,2) AD=AB+BD =(1,2,3) ∴∣AD∣=1+4+9​ =14​

Q. The two vectors $\hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + 3 \hat{j} + 5 \hat{k}$ represent the two sides $\overline{A B}$ and $\overline{A C}$ respectively of a $Δ$ ABC. The length of the median through A is

$\frac{14}{2}$

$14$

$7$

$14$

$A B = (1, 1, 1), A C = (1, 3, 5)$
$\Rightarrow BC = A C - A B = (0, 2, 4)$
Since $D$ is the mid-point of $BC$ ,
$∴ B D = (0, 1, 2)$
$A D = A B + B D$
$= (1, 2, 3)$
$∴ ∣ A D ∣ = 1 + 4 + 9$
$= 14$