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If the components of A are A_(x)=2 and A_(y)=3, and the components of B are B_(x)=-4 and B_(y)= 2, compute the components of each of the following vectors. (i) A+B (ii) A- B (iii) 2A (iv) A+ 3B

Answer» <html><body><p></p>Solution :(i) Using unit vector notation, `A= 2i - 3j and B= - <a href="https://interviewquestions.tuteehub.com/tag/4i-318769" style="font-weight:bold;" target="_blank" title="Click to know more about 4I">4I</a> + 2j`. Adding <a href="https://interviewquestions.tuteehub.com/tag/components-926700" style="font-weight:bold;" target="_blank" title="Click to know more about COMPONENTS">COMPONENTS</a>, we see that `A + B= (2+[-4])i+ ([-3]+2)j= 2i-j`. Therefore, the <a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a> <a href="https://interviewquestions.tuteehub.com/tag/component-926634" style="font-weight:bold;" target="_blank" title="Click to know more about COMPONENT">COMPONENT</a> of the sum is `-2` and the y - components is `-<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>`. <br/> (ii) `A- B= (2i-3j)-(-4i+2j)=(2-[-4])i+(-3-2)j=6i-5j`. The x-component is 6 and the y-component is `-5`. <br/> (iii) `2A=2(2i-3j)=4i-6j`. 4 and `-6` are the x- and y-components, respectively.<br/> `(iv) A+3B=(2i-3j)+3(-4i+2j)=(2+3[-4])i+(-3+3[2])j=-10i+3j. -10 and 3` are the x- and y-components, respectively.</body></html>


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