If a^{\to} = 4i^{\^}+6j^{\^} and b^{\to} = 3j^{\^}+4k^{\^} , then the vector from of the component of a^{\to} along b^{\to} is :

{18}/{10\sqrt{13} (3i^{\^}+4k^{\^})

{18}/\sqrt{13} (3i^{\^}+4k^{\^})

NIMCET 2015 Question Paper with solutions

Question : 40 of 120

Marks: +1, -0

a↖{→}

4i↖{\^}+6j↖{\^}

and

b↖{→}

3j↖{\^}+4k↖{\^}

, then the vector from of the component of

a↖{→}

along

b↖{→}

is :

Solution:

Since,

a=4i↖{⋀}+6j↖{⋀}

and

b=3i↖{⋀}+4k↖{⋀}

Vector component of a along b is

{(a⋅b)b}/b

={(4i↖{⋀}+6j↖{⋀})⋅(3i↖{⋀}+4k↖{⋀})}/(√{3^2+4^2})^2(3i↖{⋀}+4k↖{⋀})

=36/25(3i↖{⋀}+4k↖{⋀})

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