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Vector Algebra

Question
CBSEENMA12036238
Wired Faculty App

Let a, b and c be distinct non-negative numbers. If the vectors straight a straight i with hat on top space plus straight a space straight j with hat on top space plus space straight c straight k with hat on top comma space space straight i with hat on top space plus straight k with hat on top space and space straight c straight i with hat on top space plus straight c straight j with hat on top space plus straight b straight k with hat on top space 

  • the Geometric Mean of a and b

  • the Arithmetic Mean of a and b

  • equal to zero

  • the Harmonic Mean of a and b

Solution

A.

the Geometric Mean of a and b

Vector space straight a space straight i with hat on top space plus straight a straight j with hat on top space plus straight c straight k with hat on top space comma space straight i with hat on top space plus straight k with hat on top space and space straight c straight i with hat on top space plus straight c straight j with hat on top space plus straight b straight k with hat on top space are space coplanar open vertical bar table row straight a straight a straight c row 1 0 1 row straight c straight c straight b end table close vertical bar space equals space 0 rightwards double arrow space straight c squared space equals ab therefore space straight a comma straight b comma straight c space are space in space straight G. straight P

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