Question

if vector AB=2i^-j^+k^ and vector OB=3i^-4j^+4k^ find position vector OA.​

Answer 1

Answer:

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Answer 2

Answer:

$\vec{OA}= 5(\hat{i} -\hat {j}+\hat{k})$ is the required  position vector of OA.

Step-by-step explanation:

Explanation:

Given,  $AB =2\hat{i}-\hat{j}+\hat{k}$ (i)

         $OB = 3\hat{i}-4\hat{j}+4\hat{k}$.(ii)

Let ABO be triangle in which coordinates of AB and OB is given

$(2\hat{i},-\hat{j},\hat{k})$ and $(3\hat{i},-4\hat{j},4\hat{k})$ respectively .

let us assume that coordinate of OA is $(x\vec{i},y\vec{j},z\vec{k})$

As we know ,

$\vec{0A}=\vec{AB}+\vec{OB}$   ...........(iii)

Step1:

Position vector of   AB = $2\hat{i}-\hat{j}+\hat{k}$

and   the position vector of OB = $3\hat{i}-4\hat{j}+4\hat{k}$

which is given in the question .

Now, put the value of AB and OB in equation (iii)  

then,

$\vec{OA}= (2\hat{i} -\hat {j}+\hat{k}) +(3\hat{i}-4\hat{j}+4\hat{k})$

$\vec{OA}= 5(\hat{i} -\hat {j}+\hat{k})$

Final answer :

Hence , the position vector of $\vec{OA}= 5(\hat{i} -\hat {j}+\hat{k})$.