SATHEE: Complex Numbers 3 Question 7

Complex Numbers 3 Question 7

7.

If $a, b, c$ and $u, v, w$ are the complex numbers representing the vertices of two triangles such that $c = (1 - r) a + r b$ and $w = (1 - r) u + r v$ , where $r$ is a complex number, then the two triangles

$(1985, 2 M)$

(a) have the same area

(b) are similar

(d) None of these

Show Answer

Answer:

Correct Answer: 7. (b)

Solution:

Since $a, b, c$ and $u, v, w$ are the vertices of two triangles.

Also, $c = (1 - r) a + r b$

and $w = (1 - r) u + r v$

consider $| \begin{matrix} a & u & 1 \\ b & v & 1 \\ c & w & 1 \end{matrix} |$

Applying $R_{3} \to R_{3} - [(1 - r) R_{1} + r R_{2}]$

= $| \begin{matrix} a & u & 1 \\ b & v & 1 \\ c - (1 - r) a - r b & w - (1 - r) u - r v & 1 - (1 - r) - r \end{matrix} |$

$\begin{aligned} = | \begin{array}{c} a & u & 1 \\ b & v & 1 \\ 0 & 0 & 0 \end{array} | = 0 \end{aligned}$

Complex Numbers 3 Question 7

7.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

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Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Complex Numbers 3 Question 7

7.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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