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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?

1 Answer

2 votes

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.

User Kerene
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