If A -2 -4 -5 k- the direction of cosines of the vector A areA- 3-45- 2-45 and 5-45B- 1-45- 2-45 and 3-45C- 2-45- 4-45 and 5-45D- 4-45- 0 and 4-45

The correct option is C 2/√(45),4/√(45) and 5/√(45)A⃗=2î+4ĵ 5k̂ ∴ |A⃗|=√((2)^2+(4)^2+( 5)^2)=√(45) ∴ cos α = 2/√(45), cos β = 4/√(45),cos γ = 5/√(45) ...

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Byju's Answer

Standard XII

Physics

Addition and Subtraction in Unit Vector Notation

If A =2 î+4 ĵ...

Question

If $\to A = 2^i + 4^j - 5^k$ the direction of cosines of the vector
$\to A$ are

\frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}

and

\frac{5}{\sqrt{45}}

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\frac{1}{\sqrt{45}}, \frac{2}{\sqrt{45}}

and

\frac{3}{\sqrt{45}}

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\frac{4}{\sqrt{45}}, 0

and

\frac{4}{\sqrt{45}}

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\frac{3}{\sqrt{45}}, \frac{2}{\sqrt{45}}

and

\frac{5}{\sqrt{45}}

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Solution

The correct option is A $\frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}$ and $\frac{5}{\sqrt{45}}$
$\to A = 2^i + 4^j - 5^k ∴ | \to A | = \sqrt{(2)^{2} + (4)^{2} + (- 5)^{2}} = \sqrt{45}$
$∴ c o s α = \frac{2}{\sqrt{45}}, c o s β = \frac{4}{\sqrt{45}}, c o s γ = \frac{- 5}{\sqrt{45}}$

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If →A=2^i+4^j−5^k the direction of cosines of the vector →A are

The correct option is A 2√45,4√45 and 5√45→A=2^i+4^j−5^k ∴|→A|=√(2)2+(4)2+(−5)2=√45 ∴cosα=2√45,cosβ=4√45,cosγ=−5√45

If $\to A = 2^i + 4^j - 5^k$ the direction of cosines of the vector
$\to A$ are

The correct option is A $\frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}$ and $\frac{5}{\sqrt{45}}$
$\to A = 2^i + 4^j - 5^k ∴ | \to A | = \sqrt{(2)^{2} + (4)^{2} + (- 5)^{2}} = \sqrt{45}$
$∴ c o s α = \frac{2}{\sqrt{45}}, c o s β = \frac{4}{\sqrt{45}}, c o s γ = \frac{- 5}{\sqrt{45}}$