Archive
6th of March 2017
Mathematics
Q:

Ifa with rightwards arrow on topandb with rightwards arrow on topare two unit vectors then find the angle betweena with rightwards arrow on topandb with rightwards arrow on topgiven that 3 a with rightwards arrow on top- b with rightwards arrow on topis a unit vector

Ahuja8087 Ahuja - CBSE - Class XII Science

Monday, March 06, 2017 at 16:37:PM

A:

Hi student, I have solved the question as you have posted. But I feel the '3' should be square root of 3.

Kindly check. If not, then below is the solution. If yes, then follow the same process, and towards, the end you will get

begin mathsize 12px style straight theta equals cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses space and space hence space straight theta equals straight pi over 6 end style

begin mathsize 12px style open vertical bar straight a with rightwards arrow on top close vertical bar equals 1 comma space open vertical bar straight b with rightwards arrow on top close vertical bar equals 1
open vertical bar stack 3 straight a with rightwards arrow on top minus straight b with rightwards arrow on top close vertical bar equals 1
rightwards double arrow open vertical bar stack 3 straight a with rightwards arrow on top minus straight b with rightwards arrow on top close vertical bar squared equals 1 squared
rightwards double arrow open parentheses 3 straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses times open parentheses 3 straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses equals 1
rightwards double arrow 3 straight a with rightwards arrow on top times 3 straight a with rightwards arrow on top minus 3 straight a with rightwards arrow on top times straight b with rightwards arrow on top minus straight b with rightwards arrow on top times 3 straight a with rightwards arrow on top plus straight b with rightwards arrow on top times straight b with rightwards arrow on top equals 1
rightwards double arrow 9 space left parenthesis 1 right parenthesis minus space 6 space straight a with rightwards arrow on top times straight b with rightwards arrow on top plus 1 squared equals 1
rightwards double arrow 9 minus space 6 space straight a with rightwards arrow on top times straight b with rightwards arrow on top plus 1 equals 1
rightwards double arrow straight a with rightwards arrow on top times straight b with rightwards arrow on top equals 9 over 6
rightwards double arrow straight a with rightwards arrow on top times straight b with rightwards arrow on top equals negative 3 over 2
open vertical bar straight a with rightwards arrow on top close vertical bar equals 1 comma space open vertical bar straight b with rightwards arrow on top close vertical bar equals 1
open vertical bar stack 3 straight a with rightwards arrow on top minus straight b with rightwards arrow on top close vertical bar equals 1
rightwards double arrow open vertical bar stack 3 straight a with rightwards arrow on top minus straight b with rightwards arrow on top close vertical bar squared equals 1 squared
rightwards double arrow open parentheses 3 straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses times open parentheses 3 straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses equals 1
rightwards double arrow 3 straight a with rightwards arrow on top times 3 straight a with rightwards arrow on top minus 3 straight a with rightwards arrow on top times straight b with rightwards arrow on top minus straight b with rightwards arrow on top times 3 straight a with rightwards arrow on top plus straight b with rightwards arrow on top times straight b with rightwards arrow on top equals 1
rightwards double arrow 9 space left parenthesis 1 right parenthesis minus space 6 space straight a with rightwards arrow on top times straight b with rightwards arrow on top plus 1 squared equals 1
rightwards double arrow 9 minus space 6 space straight a with rightwards arrow on top times straight b with rightwards arrow on top plus 1 equals 1
rightwards double arrow straight a with rightwards arrow on top times straight b with rightwards arrow on top equals 9 over 6
rightwards double arrow straight a with rightwards arrow on top times straight b with rightwards arrow on top equals 3 over 2
rightwards double arrow open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar cosθ equals 3 over 2
rightwards double arrow cosθ equals 3 over 2
rightwards double arrow straight theta equals cos to the power of negative 1 end exponent open parentheses 3 over 2 close parentheses
end style

Monday, March 06, 2017 at 17:49:PM