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  • Let <img alt="\overrightarrow{a}= 3\hat{i}-4\hat{j}+5\hat{k}" src="https://learn.careers360.com/latex-image/?%5Coverrightarrow%7Ba%7D%3D%203%5Chat%7Bi%7D-4%5Chat%7Bj%7D&plus;5%5Chat%7Bk%7D

Let \overrightarrow{a}= 3\hat{i}-4\hat{j}+5\hat{k} and \overrightarrow{b}= -\hat{i}+4\hat{j}+4\hat{k} then \overrightarrow{a}\cdot \overrightarrow{b} equals

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

As we learn

Dot Product of two vectors -

\vec{a}.\vec{b}=a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}

- wherein

\vec{a}=a_{1}\hat{i}+a_{2}\hat{j}+a_{3}\hat{k}

\vec{b}=b_{1}\hat{i}+b_{2}\hat{j}+b_{3}\hat{k}

 

 \vec{a}=3\hat{i}-4\hat{j}+5\hat{k}\Rightarrow a_{1}=3,a_{2}=-4, a_{3}=5

\vec{b}=-1\hat{i}+4\hat{j}+4\hat{k}\Rightarrow b_{1}=-1,b_{2}=4, b_{3}=4

\therefore a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}=1

\therefore \vec{a}\cdot \vec{b}=1

Posted by

Divya Prakash Singh

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