Question

The position vectors of the points $A$ and $B$ are respectively $3\hat{i}-5\hat{j}+2\hat{k}$ and $\hat{i}+\hat{j}-\hat{k}$. What is the length of $AB$?

• A. $11$
• B. $9$
• C. $7$
• D. $6$

Answer 1

Answer: (C)

$7$

Now, for vectors

$A=a_1\hat{i}+b_1\hat{j}+c_1\hat{k}$

$B=a_2\hat{i}+b_2\hat{j}+c_2\hat{k}$

length of $AB=\sqrt{(a_2-a_1{)}^2+(b_2-b_1{)}^2+(c_2-c_1{)}^2}$

So, for given vectors

Length of AB $=\sqrt{(3-1{)}^2+(-5-1{)}^2+(2+1{)}^2}$

$=\sqrt{4+36+9}$

$=7$