Maths-
General
Easy

Question

left parenthesis a with not stretchy bar on top times ı with not stretchy bar on top right parenthesis squared plus left parenthesis a with not stretchy bar on top times ȷ with not stretchy bar on top right parenthesis squared plus left parenthesis a with not stretchy bar on top times k with not stretchy bar on top right parenthesis squared equals

  1. a with not stretchy bar on top squared
  2. 2 a with not stretchy bar on top squared
  3. 3 a with not stretchy bar on top squared
  4. 4 a with not stretchy bar on top squared

hintHint:

In this question, we have to find the value of left parenthesis a with not stretchy bar on top times ı with not stretchy bar on top right parenthesis squared plus left parenthesis a with not stretchy bar on top times ȷ with not stretchy bar on top right parenthesis squared plus left parenthesis a with not stretchy bar on top times k with not stretchy bar on top right parenthesis squared equals. we will solve this using vector theorem. For this we will use dot product and scalar product i.e.,i with hat on top. i with hat on top equals j with hat on top. j with hat on top equals k with hat on top. k with hat on top equals 1 space a n d space top enclose a. top enclose b equals space open vertical bar top enclose a close vertical bar. open vertical bar top enclose b close vertical bar cos theta and the property that sum of square of direction cosine is 1.

The correct answer is: a with not stretchy bar on top squared


    space space left parenthesis a with not stretchy bar on top times ı with not stretchy bar on top right parenthesis squared plus left parenthesis a with not stretchy bar on top times ȷ with not stretchy bar on top right parenthesis squared plus left parenthesis a with not stretchy bar on top times k with not stretchy bar on top right parenthesis to the power of 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis top enclose a. top enclose b equals space open vertical bar top enclose a close vertical bar. open vertical bar top enclose b close vertical bar cos theta right parenthesis end exponent
equals space open square brackets open vertical bar a close vertical bar. open vertical bar i with overparenthesis on top close vertical bar. cos space l close square brackets squared plus space open square brackets open vertical bar a close vertical bar. open vertical bar j with overparenthesis on top close vertical bar. c o s space m close square brackets squared plus space open square brackets open vertical bar a close vertical bar. open vertical bar k with overparenthesis on top close vertical bar. cos space n close square brackets squared space space space space left parenthesis i with hat on top. i with hat on top equals j with hat on top. j with hat on top equals k with hat on top. k with hat on top equals 1 right parenthesis
equals open square brackets open vertical bar top enclose a close vertical bar squared. cos squared l close square brackets plus open square brackets open vertical bar top enclose a close vertical bar squared. cos squared m close square brackets plus open square brackets open vertical bar a with bar on top close vertical bar squared cos space n close square brackets
equals open vertical bar a with bar on top close vertical bar squared open square brackets cos squared l plus cos squared m plus cos squared n close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses s u m space o f space s q u a r e space o f space d i r e c t i o n space cos i n e space i s space 1 close parentheses
equals open vertical bar a with bar on top close vertical bar squared open square brackets 1 close square brackets
equals open vertical bar a with bar on top close vertical bar squared

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