The vectors overrightarrow{AB} = 3hat{i} + 4h | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $D$ be the midpoint of $BC$. The median through $A$ is the vector $\overrightarrow{AD}$.Since $D$ is the midpoint of $BC$,we have $\overrighta

Vedclass · Accepted Answer

$\sqrt{33}$

Vedclass · Answer

(C) Let $D$ be the midpoint of $BC$. The median through $A$ is the vector $\overrightarrow{AD}$.Since $D$ is the midpoint of $BC$,we have $\overrightarrow{AD} = \frac{1}{2}(\overrightarrow{AB} + \overrightarrow{AC})$.Substituting the given vectors:$\overrightarrow{AD} = \frac{1}{2}((3\hat{i} + 4\hat{k}) + (5\hat{i} - 2\hat{j} + 4\hat{k}))$$\overrightarrow{AD} = \frac{1}{2}(8\hat{i} - 2\hat{j} + 8\hat{k}) = 4\hat{i} - \hat{j} + 4\hat{k}$.The length of the median is the magnitude of $\overrightarrow{AD}$:$|\overrightarrow{AD}| = \sqrt{4^2 + (-1)^2 + 4^2} = \sqrt{16 + 1 + 16} = \sqrt{33}$.

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

Similar Questions

How many moles of $KMnO_4$ are required to oxidize $1 \ mol$ of $FeC_2O_4$ in an acidic medium?

The potential difference between two parallel plates is $10^4 ~V$. If the plates are separated by $0.5 ~cm$,the force on an electron between the plates is

The solution of the differential equation $\frac{dy}{dx} - y \tan x = e^x \sec x$ is

$A$ particle is executing simple harmonic motion with an amplitude $A$ and time period $T$. The displacement of the particle after $2T$ time from its initial position is

What is the function of mycorrhiza?

Vedclass Test Series

Exam Paper Generator

Online Exam Module