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Mathematics Question on Vector Algebra

Let π‘Žβ†’=4𝑖^+3𝑗^Λ†\overrightarrow π‘Ž =4\hat 𝑖+3\hat 𝑗ˆ and 𝑏→=3𝑖^βˆ’4𝑗^\overrightarrow 𝑏 =3\hat π‘–βˆ’4\hat 𝑗+5π‘˜^5\hat π‘˜. If 𝑐→\overrightarrow 𝑐 is a vector such that 𝑐→⋅(π‘Žβ†’Γ—π‘β†’βƒ—)+25=0\overrightarrow 𝑐 β‹…(\overrightarrow π‘Ž Γ—\overrightarrow𝑏⃗ )+25=0, 𝑐→⋅(𝑖^+𝑗^+π‘˜^)=4\overrightarrow𝑐 β‹…(\hat𝑖+\hat𝑗+ \hatπ‘˜)=4, and projection of 𝑐→\overrightarrow𝑐 on π‘Žβ†’\overrightarrowπ‘Ž is 11 , then the projection of 𝑐→\overrightarrow 𝑐 on 𝑏→\overrightarrow 𝑏 equals

A

52\frac{5}{\sqrt 2}

B

15\frac{1}{5}

C

12\frac{1}{\sqrt 2}

D

12\frac{1}{\sqrt 2}

Answer

52\frac{5}{\sqrt 2}

Explanation

Solution

The Correct Option is (A): 52\frac{5}{\sqrt 2}