Let a circle C in complex plane pass through the points z1 = 3 + 4i, z2 = 4 + 3i and z3 = 5i. If <math> <mrow> <mi>z</mi> <mrow> <mo>(</mo> <mrow> <mo>≠</mo> <msub> <mrow> <mi>z</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </math> is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then arg(z) is equal to:

2 − 4 = − 1 2 y – 4 = 2 (x – 3)y = 2x – 2x2 + (2x – 2)2 = 25 5 x 2 − 8 x − 2 1 = 0 z ( − 7 5 , − 2 4 5 )

Let a circle C in complex plane pass through the points z1 = 3 + 4i, z2 = 4 + 3i and z3 = 5i. If <math> <mrow> <mi>z</mi> <mrow> <mo>(</mo> <mrow> <mo>≠</mo> <msub> <mrow> <mi>z</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </math> &nbsp;is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then arg(z) is equal to:

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Maths NCERT Exemplar Solutions Class 11th Chapter Two Maths Class 12th Ncert Solutions Maths class 12th

Let a circle C in complex plane pass through the points z₁ = 3 + 4i, z₂ = 4 + 3i and z₃ = 5i. If $z (\neq z_{1})$ is a point on C such that the line through z and z₁ is perpendicular to the line through z₂ and z₃, then arg(z) is equal to:

Option 1 -

$t a n^{- 1} (\frac{2}{\sqrt[]{5}}) - π$

Option 2 -

$t a n^{- 1} (\frac{24}{7}) - π$

Option 3 -

$t a n^{- 1} (3) - π$

Option 4 -

$t a n^{- 1} (\frac{3}{4}) - π$

2 Views | Posted 3 weeks ago

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1 Answer

Answered by

Raj Pandey | Contributor-Level 9

3 weeks ago

Correct Option - 4

Detailed Solution:

$\frac{2}{- 4} = \frac{- 1}{2}$

y – 4 = 2 (x – 3)

y = 2x – 2

x² + (2x – 2)² = 25

$5 x^{2} - 8 x - 21 = 0$

$z (\frac{- 7}{5}, \frac{- 24}{5})$

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Let a circle C in complex plane pass through the points z₁ = 3 + 4i, z₂ = 4 + 3i and z₃ = 5i. If $z (\neq z_{1})$ is a point on C such that the line through z and z₁ is perpendicular to the line through z₂ and z₃, then arg(z) is equal to:

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Let a circle C in complex plane pass through the points z1 = 3 + 4i, z2 = 4 + 3i and z3 = 5i. If z ( ≠ z 1 ) is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then arg(z) is equal to:

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Let a circle C in complex plane pass through the points z₁ = 3 + 4i, z₂ = 4 + 3i and z₃ = 5i. If $z (\neq z_{1})$ is a point on C such that the line through z and z₁ is perpendicular to the line through z₂ and z₃, then arg(z) is equal to: