Find the projection of the vector - - 3- - k- on the vector 7- - - - 8k-

Let a⃗ = î + 3ĵ + 7k̂ and b⃗ = 7î ĵ + 8k̂ Projection of a⃗ on b⃗ = a⃗ . b⃗|b⃗| = (î + 3ĵ + 7k̂)· (7î ĵ + 8k̂)√(49 + 1 + 64) = 7 ...

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Standard XII

Mathematics

Applications of Dot Product

Find the proj...

Question

Find the projection of the vector $^i + 3^j +^k$ on the vector $7^i -^j + 8^k$ .

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Solution

Let $\to a =^i + 3^j + 7^k$ and $\to b = 7^i -^j + 8^k$
Projection of $\to a$ on $\to b = \frac{\to a . \to b}{| \to b |}$
$= \frac{(^i + 3^j + 7^k) \cdot (7^i -^j + 8^k)}{\sqrt{49 + 1 + 64}} = \frac{7 - 3 + 56}{\sqrt{114}}$
$= \frac{60}{\sqrt{114}}$ .

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Find the projection of the vector ^i+3^j+^k on the vector 7^i−^j+8^k.

Let →a=^i+3^j+7^k and →b=7^i−^j+8^kProjection of →a on →b=→a.→b|→b|=(^i+3^j+7^k)⋅(7^i−^j+8^k)√49+1+64=7−3+56√114=60√114.

Find the projection of the vector $^i + 3^j +^k$ on the vector $7^i -^j + 8^k$ .

Let $\to a =^i + 3^j + 7^k$ and $\to b = 7^i -^j + 8^k$
Projection of $\to a$ on $\to b = \frac{\to a . \to b}{| \to b |}$
$= \frac{(^i + 3^j + 7^k) \cdot (7^i -^j + 8^k)}{\sqrt{49 + 1 + 64}} = \frac{7 - 3 + 56}{\sqrt{114}}$
$= \frac{60}{\sqrt{114}}$ .