3 years ago

Geometry help , only answer if your sure please. The question is in the attached

Mathematics

2 answers:

Usimov [2.4K]3 years ago

7 0

Angle A and E would be the same since they are the same type of angle.

o-na [289]3 years ago

5 0

the answer is "B"

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

Tomtit [17]

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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