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

#10; #10;Given vector #10; #10; #10; #10; #160; #10;a=i+3ĵ+7k̂ #10; #10; #160; =7î ĵ+8k̂ #10; #10; #160;Now ,projection ...

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Standard XII

Mathematics

Applications of Dot Product

Find the proj...

Question

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

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Solution

Given vector

$\to a = ˆ i + 3^j + 7^k$

$= 7^i -^j + 8^k$

Now ,projection of vector $\to a$ on vector $\to b$

$= \frac{\to a . \to b}{| b |}$

$= \frac{(ˆ i + 3^j + 7^k) . (7 \to i -^j + 8^k)}{∣ ∣ ∣ 7 \to i -^j + 8^k ∣ ∣ ∣}$

$= \frac{7 - 3 + 56}{\sqrt{7^{2} + {(- 1)}^{2} + 8^{2}}} = \frac{60}{\sqrt{49 + 64 + 1}}$

$= \frac{60}{\sqrt{114}}$

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

Given vector →a=ˆi+3^j+7^k =7^i−^j+8^k Now ,projection of vector →a on vector →b =→a.→b|b| =(ˆi+3^j+7^k).(7→i−^j+8^k)∣∣∣7→i−^j+8^k∣∣∣ =7−3+56√72+(−1)2+82=60√49+64+1 =60√114

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