Let a - - - 2- - k- b - - - - k- and - - - - - - k- A vector in the plane of a and b whose projection on c is 1-3- is

Let a #160; = i + 2j + k #160; #160; #160; #160; #160; #160; b #160; = i j + k #160; #160; #160; c #160; = i + j ...

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Byju's Answer

Standard XII

Mathematics

Properties of Conjugate of a Complex Number

Let a = î +...

Question

Let $¯ ¯ ¯ a =^i + 2^j +^k$ , $¯ ¯ b =^i -^j +^k$ and $^c =^i +^j -^k$ . A vector in the plane of $¯ ¯ ¯ a$ and $¯ ¯ b$ whose projection on $¯ ¯ c$ is $\frac{1}{\sqrt{3}}$ , is

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Solution

Let $¯ ¯ ¯ a = ˆ i + 2 ˆ j + ˆ k$

$¯ ¯ b = ˆ i - ˆ j + ˆ k$
$¯ ¯ c = ˆ i + j - ˆ k$
$¯ ¯ ¯ a . ¯ ¯ b = 1 - 2 + 1 = 0$
Projection= $\frac{¯ ¯ ¯ a . ¯ ¯ b}{∣ ∣ ¯ ¯ c ∣ ∣}$
$= \frac{0}{\sqrt{1^{2} + 1^{2} + 1^{2}}}$
Hence we get,
$= \frac{0}{\sqrt{3}}$

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Let ¯¯¯a=^i+2^j+^k, ¯¯b=^i−^j+^k and ^c=^i+^j−^k. A vector in the plane of ¯¯¯a and ¯¯b whose projection on ¯¯c is 1√3, is

Let ¯¯¯a=ˆi+2ˆj+ˆk ¯¯b=ˆi−ˆj+ˆk ¯¯c=ˆi+j−ˆk ¯¯¯a.¯¯b=1−2+1=0Projection=¯¯¯a.¯¯b∣∣¯¯c∣∣ =0√12+12+12Hence we get, =0√3

Let $¯ ¯ ¯ a =^i + 2^j +^k$ , $¯ ¯ b =^i -^j +^k$ and $^c =^i +^j -^k$ . A vector in the plane of $¯ ¯ ¯ a$ and $¯ ¯ b$ whose projection on $¯ ¯ c$ is $\frac{1}{\sqrt{3}}$ , is

Let $¯ ¯ ¯ a = ˆ i + 2 ˆ j + ˆ k$

$¯ ¯ b = ˆ i - ˆ j + ˆ k$
$¯ ¯ c = ˆ i + j - ˆ k$
$¯ ¯ ¯ a . ¯ ¯ b = 1 - 2 + 1 = 0$
Projection= $\frac{¯ ¯ ¯ a . ¯ ¯ b}{∣ ∣ ¯ ¯ c ∣ ∣}$
$= \frac{0}{\sqrt{1^{2} + 1^{2} + 1^{2}}}$
Hence we get,
$= \frac{0}{\sqrt{3}}$