A vector r- is equally inclined with the coordinate axes- If the tip of r- is in the first octant and -r-3 then r- is

The correct option is D (î+ĵ+k̂) r⃗=λî+βĵ+γk̂ r⃗·î=r⃗·ĵ=r⃗·k̂ λ =β =γ | r⃗ |=√(3λ ^2) λ =1 r⃗=î+ĵ+k̂ ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

A vector r⃗...

Question

A vector $\to r$ is equally inclined with the coordinate axes. If the tip of $\to r$ is in the first octant and $| \to r | = \sqrt{3}$ then $\to r$ is

2 \sqrt{3} (^i -^j +^k)

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2 \sqrt{3} (-^i +^j +^k)

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2 \sqrt{3} (^i +^j -^k)

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(^i +^j +^k)

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Solution

The correct option is D $(^i +^j +^k)$
$\to r = λ^i + β^j + γ^k$
$\to r \cdot^i = \to r \cdot^j = \to r \cdot^k$
$λ = β = γ$
$| \to r | = \sqrt{3 λ^{2}}$
$λ = 1$
$\to r =^i +^j +^k$

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A vector →r is equally inclined with the coordinate axes. If the tip of →r is in the first octant and |→r|=√3 then →r is

The correct option is D (^i+^j+^k)→r=λ^i+β^j+γ^k→r⋅^i=→r⋅^j=→r⋅^kλ=β=γ|→r|=√3λ2λ=1→r=^i+^j+^k

A vector $\to r$ is equally inclined with the coordinate axes. If the tip of $\to r$ is in the first octant and $| \to r | = \sqrt{3}$ then $\to r$ is

The correct option is D $(^i +^j +^k)$
$\to r = λ^i + β^j + γ^k$
$\to r \cdot^i = \to r \cdot^j = \to r \cdot^k$
$λ = β = γ$
$| \to r | = \sqrt{3 λ^{2}}$
$λ = 1$
$\to r =^i +^j +^k$