Question

Consider points A(1,0, −5) and B(2, −3,6).

Answer 1

Answer:  a) $\hat{i}-3\hat{j}+11\hat{k}$ b)√131.

Step-by-step explanation:

Since we have given that

A(1,0,-5), is rewritten in vector form is given by

$1\hat{i}-5\hat{k}$

B(5,-3,6) is rewritten in vector form is given by

$2\hat{i}-3\hat{j}+6\hat{k}$

a. What is the component form of AB?

So, it becomes,

$\vec{AB}=(2-1)\hat{i}+(-3-0)\hat{j}+(6+5)\hat{k}\\\\\vec{AB}=\hat{i}-3\hat{j}+11\hat{k}$

b. What is the magnitude of AB?

$\mid AB\mid=\sqrt{1^2+(-3)^2+11^2}\\\\\mid AB\mid=\sqrt{1+9+121}\\\\\mid AB\mid=\sqrt{131}$

Hence, a) $\hat{i}-3\hat{j}+11\hat{k}$ b)√131.