Maths-
General
Easy

Question

Let stack a with rightwards arrow on top equals 2 stack i with hat on top plus stack j with hat on top minus 2 stack k with hat on top and stack b with rightwards arrow on top equals stack i with hat on top plus stack j with hat on top. If stack c with rightwards arrow on top is a vector such that stack a with rightwards arrow on top. stack c with rightwards arrow on top equals open vertical bar stack c with rightwards arrow on top close vertical bar comma open vertical bar stack c with rightwards arrow on top minus stack a with rightwards arrow on top close vertical bar=2 square root of 2and the angle between open parentheses stack a with rightwards arrow on top cross times stack b with rightwards arrow on top close parentheses and stack c with rightwards arrow on top is 300, then find the value ofopen vertical bar open parentheses stack a with rightwards arrow on top cross times stack b with rightwards arrow on top close parentheses cross times stack c with rightwards arrow on top close vertical bar.

  1. 2 over 3    
  2. 3 over 2    
  3. 2    
  4. 3    

The correct answer is: 3 over 2


    open vertical bar open parentheses stack a with rightwards arrow on top cross times stack b with rightwards arrow on top close parentheses cross times stack c with rightwards arrow on top close vertical bar= open vertical bar stack a with rightwards arrow on top cross times stack b with rightwards arrow on top close vertical bar short rightwards arrow over leftwards arrow vertical line stack c with rightwards arrow on top vertical line sin 300
    stack a with rightwards arrow on top cross times stack b with rightwards arrow on top equals open vertical bar table row i j k row 2 1 cell negative 2 end cell row 1 1 0 end table close vertical bar equals negative 2 i plus 2 j plus k Þ vertical line stack a with rightwards arrow on top cross times stack b with rightwards arrow on top vertical line equals 3
    vertical line stack c with ⃑ on top minus stack a with ⃑ on top vertical line to the power of 2 end exponent= 8 Þ vertical line stack c with ⃑ on top vertical line to the power of 2 end exponent plus vertical line stack a with ⃑ on top vertical line to the power of 2 end exponent minus 2 stack c with ⃑ on top. stack a with ⃑ on top = 8
    Þ vertical line stack c with ⃑ on top vertical line to the power of 2 end exponent minus 2 vertical line stack c with ⃑ on top vertical line plus 1 equals 0Þ vertical line stack c with ⃑ on top vertical line equals 1 Þ open vertical bar open parentheses stack a with rightwards arrow on top cross times stack b with rightwards arrow on top close parentheses cross times stack c with rightwards arrow on top close vertical bar = 1. 3. fraction numerator 1 over denominator 2 end fraction = fraction numerator 3 over denominator 2 end fraction.

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