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Let a = 2 i + j - 2 k, b = i + j and c = a b. Let d be a vector such that | d - a| = 11, | c d| = 3 and the angle between c and d is 4. Then a d is equal to
(1) 0
c = a b = vmatrix i & j & k \ 2 & 1 & -2 \ 1 & 1 & 0 vmatrix = 2 i - 2 j + k
| c| = 4 + 4 + 1 = 3
| c d| = | c|| d| 4 = 3
3| d| 1 2 = 3
| d| = 2
| d - a|2 = | d|2 + | a|2 - 2 a d = 11
2 + 9 - 2 a d = 11
a d = 0
Answer: (1)
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