If x- y- are two non collinear vectors and a- b- c represent the sides of -ABC satisfying a-bx-b-cy-c-ax-y-0 then -ABC is-

The correct option is A An acute angle triangle [ (a b)x⃗ +(b c)y⃗ +(c a)(x⃗×y⃗ )=0; #160; a b=b c=c a=0; #160; ] ...

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Byju's Answer

Standard IX

Mathematics

Properties of Isosceles Triangle

If x⃗ y...

Question

If $\to x$ & $\to y$ are two non collinear vectors and a, b, c represent the sides of $Δ$ ABC satisfying $(a - b) \to x + (b - c) \to y + (c - a) (\to x \times \to y) = 0$ then $Δ$ ABC is?

An acute angle triangle

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An obtuse angle triangle

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A right angle triangle

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A scalene triangle

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Solution

The correct option is A An acute angle triangle
$\begin{matrix} (a - b) \to x + (b - c) \to y + (c - a) (\to x \times \to y) = 0 a - b = b - c = c - a = 0 \end{matrix}$
therefore,
$a = b = c$
Hence, the triangle is An acute angle
Therefore,
Option $A$ is correct.

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Similar questions

Q. If

\to x

\to y

are two non collinear vectors and a, b, c represent the sides of a

Δ A B C

satisfying

(a - b) \to x + (b - c) \to y + (c - a) (\to x \times \to y) = 0

then

Δ A B C

Q. If

\to x

and

\to y

are two non-collinear vectors and

a, b

and

c

represent the sides of a

Δ A B C

satisfying

(a - b) \to x + (b - c) \to y + (c - a) (\to x \times \to y) = 0

, then

Δ A B C

(

where

\to x \times \to y

is perpendicular to the plane of

\to x

and

\to y)

Q. If

\to x

and

\to y

are two non-parallel vectors and

A B C

is a triangle with side lengths

a, b

and

c

satisfying

(20 a - 15 b) \to x + (15 b - 12 c) \to y + (12 c - 20 a) (\to x \times \to y) = \to 0

, then triangle

A B C

Q. If

\to x

and

\to y

are two non-collinear vectors and

A B C

is a triangle with side lengths

a, b

and

c

satisfying

(20 a - 15 b) \to x + (15 b - 12 c) \to y + (12 c - 20 a) (\to x \times \to y) = \to 0

, then triangle

A B C

Q. If

\to x

and

\to y

are two non-collinear vectors and

A B C

is a triangle with sides

a, b, c

satisfying

(20 a - 15 b) \to x + (15 b - 12 c) \to y + (12 c - 20 a)

(\to x \times \to y) = \to 0

, then the triangle

A B C

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If →x & →y are two non collinear vectors and a, b, c represent the sides of ΔABC satisfying (a−b)→x+(b−c)→y+(c−a)(→x×→y)=0 then ΔABC is?

The correct option is A An acute angle triangle(a−b)→x+(b−c)→y+(c−a)(→x×→y)=0a−b=b−c=c−a=0therefore,a=b=cHence, the triangle is An acute angle Therefore, Option A is correct.

If $\to x$ & $\to y$ are two non collinear vectors and a, b, c represent the sides of $Δ$ ABC satisfying $(a - b) \to x + (b - c) \to y + (c - a) (\to x \times \to y) = 0$ then $Δ$ ABC is?

The correct option is A An acute angle triangle
$\begin{matrix} (a - b) \to x + (b - c) \to y + (c - a) (\to x \times \to y) = 0 a - b = b - c = c - a = 0 \end{matrix}$
therefore,
$a = b = c$
Hence, the triangle is An acute angle
Therefore,
Option $A$ is correct.