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Two vectors are given by

$$\vec{a} = 3.0\,\hat{i} − 2.5\,\hat{j} + 1.0 \,\hat{k}$$ and $$\vec{b} = −1.0\,\hat{i} + 1.0\,\hat{j} + 6.0\,\hat{k} $$

In unit-vector notation, find the following.

(a) $\vec{a}+\vec{b} =$

(b) $ \vec{a} − \vec{b} =$

(c) $\vec{c}$ such that $\vec{a}-\vec{b}+\vec{c} = 0$

How is this supposed to be solved? For a, I tried adding the columns, for $4i$, $2.5j$, $49k$, then squaring everything, and then root-squaring that. It says the answer is wrong, though.

snulty
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user366783
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1 Answers1

1

By definition we add two vectors $\vec a$ and $\vec b$ simply summing the coefficients of the same unit vector of the basis.

So, in your case:

$$ \vec a + \vec b = (3\,\hat{i} − 2.5\,\hat{j} + 1 \,\hat{k})+(−1\,\hat{i} + 1\,\hat{j} + 6\,\hat{k})=(3-1)\hat{i}+(-2.5+1)\hat{j}+(1+6)\hat{k} $$ You can see here, and use this to solve also the other questions.

Emilio Novati
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