Question

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

Answer 1

A.B=7

Explanation:

A.B=AxBx+AyBy+AzBz

=(3 x 4)+(2 x 0)+(-1 x 5)

=12-5

=7

Answer 2

Answer:
`a\cdot b= 7`

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`