The projection of vector b - c on a is Where loverrightarrow a -2 -hat i -3 hat j -4 hat k loverrightarrow b-3 hat i-3 hat j-3 hat k loverrightarrow c- hat i- hat j-3 hat k

Given, a=2î 3ĵ+4k̂ b=3î 3ĵ+3k̂ c=î+ĵ+3k̂ b+c = 4î 2ĵ+6k̂ The projection of (b+c) on a is given by, (b+c).a|a|=(4î 2ĵ+6k̂).(2î 3ĵ+4k̂)√(2^2+( 3)^2+4^2) =38√(29) ...

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Byju's Answer

Standard XII

Physics

Comparing Vectors

The projectio...

Question

The projection of vector $\to b + \to c$ on $\to a$ is _____
Where $\to a = 2^i - 3^j + 4^k \to b = 3^i - 3^j + 3^k \to c =^i +^j + 3^k$

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Solution

Given, $\to a = 2^i - 3^j + 4^k \to b = 3^i - 3^j + 3^k \to c =^i +^j + 3^k$
$\to b + \to c = 4^i - 2^j + 6^k$

The projection of $(\to b + \to c)$ on $\to a$ is given by,
$(\to b + \to c) . \frac{\to a}{| \to a |} = \frac{(4^i - 2^j + 6^k) . (2^i - 3^j + 4^k)}{\sqrt{2^{2} + (- 3)^{2} + 4^{2}}}$
$= \frac{38}{\sqrt{29}}$

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Q. If

\to a = a_{1}^i + a_{2}^j + a_{3}^k; \to b = b_{1}^i + b_{2}^j + b_{3}^k;

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and

[3 \to a + \to b, 3 \to b + \to c, 3 \to c + \to a]

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Let $\to a =^i +^j +^k, \to b =^i -^j +^k$ and $\to c =^i -^j -^k$ be three vectors. A vector $\to v$ in the plane of
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The projection of vector →b+→c on →a is _____ Where →a=2^i−3^j+4^k→b=3^i−3^j+3^k→c=^i+^j+3^k

Given, →a=2^i−3^j+4^k→b=3^i−3^j+3^k→c=^i+^j+3^k →b+→c = 4^i−2^j+6^k The projection of (→b+→c) on →a is given by, (→b+→c).→a|→a|=(4^i−2^j+6^k).(2^i−3^j+4^k)√22+(−3)2+42 =38√29

The projection of vector $\to b + \to c$ on $\to a$ is _____
Where $\to a = 2^i - 3^j + 4^k \to b = 3^i - 3^j + 3^k \to c =^i +^j + 3^k$