Answer: a) [tex]\hat{i}-3\hat{j}+11\hat{k}[/tex] b)√131.
Step-by-step explanation:
Since we have given that
A(1,0,-5), is rewritten in vector form is given by
[tex]1\hat{i}-5\hat{k}[/tex]
B(5,-3,6) is rewritten in vector form is given by
[tex]2\hat{i}-3\hat{j}+6\hat{k}[/tex]
a. What is the component form of AB?
So, it becomes,
[tex]\vec{AB}=(2-1)\hat{i}+(-3-0)\hat{j}+(6+5)\hat{k}\\\\\vec{AB}=\hat{i}-3\hat{j}+11\hat{k}[/tex]
b. What is the magnitude of AB?
[tex]\mid AB\mid=\sqrt{1^2+(-3)^2+11^2}\\\\\mid AB\mid=\sqrt{1+9+121}\\\\\mid AB\mid=\sqrt{131}[/tex]
Hence, a) [tex]\hat{i}-3\hat{j}+11\hat{k}[/tex] b)√131.
