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mina [271]
3 years ago
12

Find a.b. a=3i+2j-k, b=4i+5k

Mathematics
1 answer:
Tomtit [17]3 years ago
5 0

Answer: a\cdot b= 7

Step-by-step explanation:

We are given

a=3\hat{i}+2\hat{j}-\hat{k}

b=4\hat{i}+5\hat{k}

They can be written as

a=3\hat{i}+2\hat{j}+(-1)\hat{k}

b=4\hat{i}+0.\hat{j}+5\hat{k}

Now , the dot product of and b is given by :-

\Rightarrow\ a\cdot b= (3\hat{i}+2\hat{j}+(-1)\hat{k})\cdot(4\hat{i}+0.\hat{j}+5\hat{k})

\Rightarrow\ a\cdot b=3\cdot 4 \cdot\hat{i}\cdot\hat{i}+2\cdot0\cdot\hat{j} \cdot\hat{j}+ (-1)\cdot 5 \cdot \hat{k}\cdot \hat{k}

\Rightarrow\ a\cdot b=12 \cdot\hat{i}^2+0-5 \cdot \hat{k}^2

\Rightarrow\ a\cdot b=12 \cdot(1)+0-5 \cdot (1)[Since \hat{i}^2=\hat{k}^2=1]

\Rightarrow\ a\cdot b=12 -5=7  

Therefore , the value of the dot product a\cdot b= 7

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