If a -2- - -k- - b -3- -4- -2k- - c - -2- -2k- then the projection of a - b on c is

The correct option is A 173 a⃗+b⃗=5î 3ĵ+3k̂ Projection of a⃗+b⃗ on c⃗ is (a⃗+b⃗).c⃗|c⃗| 5+6+6√(1+4+4)=173 ...

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Applications of Dot Product

If a =2î +ĵ...

Question

If $\to a = 2^i +^j +^k, \to b = 3^i - 4^j + 2^k, \to c =^i - 2^j + 2^k$ then the projection of $\to a + \to b$ on $\to c$ is

\frac{17}{3}

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\frac{5}{3}

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\frac{4}{3}

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\frac{17}{\sqrt{43}}

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Solution

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\to a . (\to b \times \to c)

\to a = 2^i +^j + 3^k, \to b = -^i + 2^j +^k a n d \to c = 3^i +^j + 2^k

Find $\to a . (\to b \times \to c)$ , if $\to a = 2^i +^j + 3^k, \to b = -^i + 2^j +^k$ and $\to c = 3^i +^j + 2^k$ .

If \to a = 2^i + 3^j +^k, \to b =^i - 2^j +^k and \to c = - 3^i +^j + 2^k,

[\to a \to b \to c] .

(\to a + 2 \to b)

\to c

\to a = 2^i - 2^j +^k, \to b =^i + 2^j - 2^k

\to c = 2^i -^j + 4^k

\to a = 3^i - 2^j +^k,

\to b = 2^i - 4^j - 3^k, \to c = -^i + 2^j + 2^k

\to a + \to b + \to c = 4^i - 4^j

\to a =^i -^j + 2^k, \to b = 2^i + 3^j +^k, \to c =^i -^k

\to a + 2 \to b - 3 \to c

\sqrt{78}

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