If x- and y- are two non-collinear vectors and a- b and c represent the sides of a - ABC satisfying a-b x- - b - c y- - c - a x-y- - 0- then - ABC is where x-y- is perpendicular to the plane of x- and y-

The correct option is B An acute angle triangleAs x⃗, nbsp;y⃗ and x⃗× nbsp;y⃗ are non collinear vectors, vectors are linearly independent. Henc ...

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Byju's Answer

Standard XII

Mathematics

Direction Cosines

If x⃗ and ...

Question

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 $Δ A B C$ is $($ where $\to x \times \to y$ is perpendicular to the plane of $\to x$ and $\to y)$

An acute-angle triangle

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An obtuse-angled triangle

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Right-angled triangle

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A scalene triangle

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Solution

The correct option is B An acute-angle triangle
As $\to x, \to y$ and $\to x \times \to y$ are non-collinear vectors, vectors are linearly independent. Hence,
$a - b = 0 = b - c = c - a$
or $a = b = c$
Therefore, the triangle is equilateral.

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Similar questions

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

\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. Vector

\to x

is Vectors

\to x, \to y

and

\to z,

each of magnitude

\sqrt{2},

make an angle of

60^{\circ}

with each other.

\to x \times (\to y \times \to z) = \to a, \to y \times (\to z \times \to x) = \to b

and

\to x \times \to y = \to c .

Q. If

| \to x | = | \to y | = | \to x + \to y | = 1

, then

| \to x - \to y | =

_______

Q. If

\to x, \to y, \to z

are units vectors such that

\to x + \to y + \to z = \to a

(\to x \times \to y) \times \to z = \to b

\to a \cdot \to x = \frac{3}{2}, \to a \cdot \to y = \frac{7}{4}

and

| \to a | = 2,

then which of the following is FALSE?

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

The correct option is B An acute-angle triangleAs →x,→y and →x×→y are non-collinear vectors, vectors are linearly independent. Hence,a−b=0=b−c=c−aor a=b=cTherefore, the triangle is equilateral.

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 $Δ A B C$ is $($ where $\to x \times \to y$ is perpendicular to the plane of $\to x$ and $\to y)$

The correct option is B An acute-angle triangle
As $\to x, \to y$ and $\to x \times \to y$ are non-collinear vectors, vectors are linearly independent. Hence,
$a - b = 0 = b - c = c - a$
or $a = b = c$
Therefore, the triangle is equilateral.