Question

Question 9 10 pts Let A-(3.1i-2.33+1.9k) cm and B have components B, -2.7 cm, B,-1.5 cm, with no y component. What is A+B? O 1.21 cm (0.4i - 2.33+3.4k) cm CTL O 7.39 cm 3.9 cm o (5.8i -2.33+0.4k) cm Question 10 10 pts What is the magnitude (in crn of the vector (-101 + 2 8 . 2.3 k) cm? (Here k is the unit vector in the z direction .. there does not appear to be an easy way to make "k hat" in html.) Hint: the Pythagorean theorem works in three dimensions as well as two dimensions.
both questions

Answer 1

Given $\vec{A}=(3.1\hat{i} -2.3\hat{j}+1.9\hat{k})cm$ and $\vec{B}=(2.7\hat{i} +0\hat{j}-1.5\hat{k})cm$

$\vec{A}+\vec{B}=?$

$\vec{A}+\vec{B}=(3.1\hat{i} -2.3\hat{j}+1.9\hat{k}) +(2.7\hat{i} +0\hat{j}-1.5\hat{k})$

$\vec{A}+\vec{B}=(3.1+2.7)\hat{i} +(-2.3+0)\hat{j}+(1.9-1.5)\hat{k}$

$\vec{A}+\vec{B}=5.8\hat{i} -2.3\hat{j}+0.4\hat{k}$

ANSWER: Option 5

================

Magnitude of $-1.0\hat{i} +2.8\hat{j}-2.3\hat{k}$

$R=\sqrt{(-1.0)^{2}+(2.8)^{2}+(-2.3)^{2}}$

ANSWER: $R=3.759 cm$

=======================