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Vector Algebra

Question
CBSEENMA12036025
Wired Faculty App

Let bold a with hat on top space bold b with hat on top space and space bold c with hat on top space be three unit vectors such that straight a with hat on top space straight x space left parenthesis straight b with hat on top space straight x straight c with hat on top right parenthesis space equals space fraction numerator square root of 3 over denominator 2 end fraction space left parenthesis straight b with hat on top plus straight c with hat on top right parenthesis. space If space straight b with hat on top space is space not space parallel space to space stack straight c. with hat on top then the angle between bold a with bold hat on top bold space and space bold b with bold hat on top is

  • 3π/4

  • π/2

  • 2π/3

  • 5π/6

Solution

D.

5π/6

Given comma space vertical line straight a with hat on top vertical line space equals space vertical line stack straight b vertical line with hat on top space equals vertical line straight c with hat on top vertical line space equals space 1 and space space straight a with hat on top space straight x space left parenthesis straight b with hat on top space straight x space straight c with hat on top space right parenthesis equals space fraction numerator square root of 3 over denominator 2 end fraction space left parenthesis straight b with hat on top space plus space straight c with hat on top space right parenthesis Now comma space consider space straight a with hat on top space straight x space left parenthesis straight b with hat on top space straight x space straight c with hat on top space right parenthesis space equals space fraction numerator square root of 3 over denominator 2 end fraction space left parenthesis straight b with hat on top space plus space straight c with hat on top space right parenthesis rightwards double arrow space left parenthesis straight a with hat on top. straight c with hat on top right parenthesis straight b with hat on top space minus space left parenthesis straight a with hat on top. straight b with hat on top right parenthesis straight c with hat on top space equals space fraction numerator square root of 3 over denominator 2 end fraction space left parenthesis straight b with hat on top space plus fraction numerator square root of 3 over denominator 2 end fraction straight c with hat on top On space comparing comma space we space get straight a with hat on top. straight b with hat on top space equals space minus space fraction numerator square root of 3 over denominator 2 end fraction space rightwards double arrow space vertical line straight a with hat on top vertical line space vertical line straight b with hat on top space vertical line space cosθ space equals space minus fraction numerator square root of 3 over denominator 2 end fraction rightwards double arrow space cos space straight theta space equals space minus fraction numerator square root of 3 over denominator 2 end fraction space vertical line because space vertical line straight a with hat on top vertical line space equals space vertical line straight b with hat on top vertical line space equals space 1 rightwards double arrow space cos space straight theta space equals space cos space open parentheses straight pi space minus straight pi over 6 close parentheses rightwards double arrow space straight theta space equals space fraction numerator 5 straight pi over denominator 6 end fraction space

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:
y' + y = ex

Determine order and degree (if defined) of differential equations:
y'' + (y')2 + 2 y = 0

Determine order and degree (if defined) of differential equations:
y″ + 2y′ + sin y = 0

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