Question

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

a. What is the component form of AB?
b. What is the magnitude of AB?

Answer 1

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

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=√(1^2+(-3)^2+11^2)\\\\\mid AB\mid=√(1+9+121)\\\\\mid AB\mid=√(131)`

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