JEE PYQ: Vector Algebra - Question ID 892cffae8b79 (JEE Main 2021)

ID: 892cffae8b79JEE Main 2021Single Correct MCQ
What will be the projection of vector A=i^+j^+k^\overrightarrow A = \widehat i + \widehat j + \widehat k on vector B=i^+j^\overrightarrow B = \widehat i + \widehat j ?

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Step-by-step Explanation

Projection = A.BB(B^){{\overrightarrow A .\overrightarrow B } \over {\left| {\overrightarrow B } \right|}}(\widehat B)

=(i^+j^+k^).(i^+j^)2(i^+j^)2= {{(\widehat i + \widehat j + \widehat k).(\widehat i + \widehat j)} \over {\sqrt 2 }}{{(\widehat i + \widehat j)} \over {\sqrt 2 }}

=22<spanclass="katexdisplay"><spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mo>×</mo></mrow><annotationencoding="application/xtex">×</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:0.6667em;verticalalign:0.0833em;"></span><spanclass="mord">×</span></span></span></span></span>(i^+j^)2= {2 \over {\sqrt 2 }}<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">×</span></span></span></span></span>{{(\widehat i + \widehat j)} \over {\sqrt 2 }}

=(i^+j^)= (\widehat i + \widehat j)