Find the projection of a-2 b- on c- where a-2 -2 -k- b-2 -2 k- and c-2 -4 k-

Given, nbsp; a=2î 2ĵ+k̂, b=î+2ĵ 2k̂ and c=2î ĵ+4k̂ We need to find nbsp;the projection of (a+2b) on c We know that the projection of (a+2b) on c is given by ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Find the proj...

Question

Find the projection of $(\to a + 2 \to b)$ on $\to c$ where $\to a = 2^i - 2^j +^k, \to b =^i + 2^j - 2^k$ and $\to c = 2^i -^j + 4^k$

\frac{8}{\sqrt{21}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- 8}{\sqrt{21}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{6}{\sqrt{21}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- 6}{\sqrt{21}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{- 6}{\sqrt{21}}$
Given, $\to a = 2^i - 2^j +^k, \to b =^i + 2^j - 2^k$ and $\to c = 2^i -^j + 4^k$
We need to find the projection of $(\to a + 2 \to b)$ on $\to c$
We know that the projection of $(\to a + 2 \to b)$ on $\to c$ is given by $(\to a + 2 \to b) .^c$ , where $^c$ is the unit vector of $\to c$ .
So, we have
$^c = \frac{\to c}{| \to c |} = \frac{2^i -^j + 4^k}{\sqrt{2^{2} + (- 1)^{2} + 4^{2}}} = \frac{1}{\sqrt{21}} (2^i -^j + 4^k)$
Also, $(\to a + 2 \to b) = (2^i - 2^j +^k) + 2 (^i + 2^j - 2^k)$
$\Rightarrow (\to a + 2 \to b) = 4^i + 2^j - 3^k$
Hence, projection is given by
$(\to a + 2 \to b) .^c = (4^i + 2^j - 3^k) . (\frac{1}{\sqrt{21}} (2^i -^j + 4^k))$
$\Rightarrow \frac{8 - 2 - 12}{\sqrt{21}} = \frac{- 6}{\sqrt{21}}$

Suggest Corrections

Similar questions

Q. I: If

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

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

then

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

II: If

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

, then magnitude of

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

\sqrt{78}

Q. If

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

\to b = 3^i + 2^j +^k

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

\to d =^i + 2^j -^k

, then

(\to a \times \to b) \times (\to c \times \to d) =

Q. Find

\to a \cdot (\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 .

Q. If

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

and

\to c = 3^i +^j + 2^k

. Find

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

Q. If

\to a = 2^i +^j +^k

\to b =^i + 2^j + 2^k

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

and

\to a \times (\to b \times \to c) = (1 + α)^i + β (1 + α)^j + r (1 + α) (1 + β)^k

, then

Join BYJU'S Learning Program

Find the projection of (→a+2→b) on →c where →a=2^i−2^j+^k,→b=^i+2^j−2^k and →c=2^i−^j+4^k

Find the projection of $(\to a + 2 \to b)$ on $\to c$ where $\to a = 2^i - 2^j +^k, \to b =^i + 2^j - 2^k$ and $\to c = 2^i -^j + 4^k$