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Q.

Let  a¯=2i¯j¯+k¯,  b¯=i¯+2j¯k¯ and c¯=i¯+j¯2k¯ be the three vectors, A vector of the type b¯+.λc¯ for some scalarλ, whose projection on a¯ is of magnitude 23 is 

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a

2i¯+3j¯3k¯

b

2i¯+j¯+5k¯

c

2i¯+3j¯+5k¯

d

2i¯j¯+5k¯

answer is B.

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Detailed Solution

Let  d¯=b¯+λ.c¯
|d¯.a¯||a¯|=23λ=1,3
d¯=b¯+c=¯2i¯j¯+5k¯  (or)  2i¯+3j¯3k¯

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Let  a¯=2i¯−j¯+k¯,  b¯=i¯+2j¯−k¯ and c¯=i¯+j¯−2k¯ be the three vectors, A vector of the type b¯+.λ⋅c¯ for some scalarλ, whose projection on a¯ is of magnitude 23 is