Let a=2i+j-2k and b=i+j. If c is a vector such that a c= |c | , |c-a |=2 2 and the angle between a b and c is 2 3, then | (a b ) c |=

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Correct answer: B. (b) : a=2i+j-2k and b=i+j ∴a b=(ijk21-2110)=2i-2j+k |a b |= 4+4+1=3 ⇒ |c-a |^2=8 ⇒ |c |^2+ |a |^2-2a c=8 ⇒ |c |^2+9-2 |c |=8 [ ∵a c= |c | and |d |=3 ] ⇒ |c |^2-2 |c |+1=0 ⇒ ( |c |-1 )^2=0 ⇒ ( |c |=1 Now, consider, | (a b ) c |= |a b | |c | sin ⁡ 2 3 =3 1 sin ⁡ 3 ( ∵ sin ⁡ 2 3= sin ⁡( - 3)= sin ⁡ 3) = 3 32

$Let a = 2 i + j - 2 k and b = i + j . If c is a vector such that a \cdot c = | c |, | c - a | = 22 and the angle between a \times b and c is \frac{2 π}{3}, then | (a \times b) \times c | =$

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