Find dot product of a vector and b vector if a vector -2 -k- and magnitude of b vector -3 acting along c vector -k-A- undefinedB- undefinedC- undefinedD- undefined

a⃗ = î + 2 ĵ + k̂ b⃗ = λ(i+j+k) |b⃗| = 3 = √(λ^2 + λ^2+λ^2) = λ√(3) ∴λ = √(3) ∴b⃗ = √(3i) + √(3j) +√(3k) ∴a⃗.b⃗ = (i+2j+k).(√(3i) + √(3j) +√(3k)) =√(3) + 2√( ...

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Standard XII

Mathematics

Distance Formula

Find dot prod...

Question

Find dot product of a vector and b vector if a vector $=^i + 2^j +^k$ and magnitude of b vector =3 acting along c vector $=^i +^j +^k$

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Solution

$\to a =^i + 2^j +^k$
$\to b = λ (i + j + k)$
$| \to b | = 3 = \sqrt{λ^{2} + λ^{2} + λ^{2}} = λ \sqrt{3}$
$∴ λ = \sqrt{3}$
$∴ \to b = \sqrt{3 i} + \sqrt{3 j} + \sqrt{3 k}$
$∴ \to a . \to b = (i + 2 j + k) . (\sqrt{3 i} + \sqrt{3 j} + \sqrt{3 k})$
$= \sqrt{3} + 2 \sqrt{3} + \sqrt{3}$
$= \sqrt{3} (4) = 4 \sqrt{3}$

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Find dot product of a vector and b vector if a vector =^i+2^j+^k and magnitude of b vector =3 acting along c vector =^i+^j+^k

→a=^i+2^j+^k →b=λ(i+j+k) |→b|=3=√λ2+λ2+λ2=λ√3 ∴λ=√3 ∴→b=√3i+√3j+√3k ∴→a.→b=(i+2j+k).(√3i+√3j+√3k) =√3+2√3+√3 =√3(4)=4√3

Find dot product of a vector and b vector if a vector $=^i + 2^j +^k$ and magnitude of b vector =3 acting along c vector $=^i +^j +^k$