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

The correct option is A an acute angle triangle ( a b )x+ ( b c )y+ ( c a ) ( x×y )=0 #160;As #160; x,y amp; #160; ( x×y ) are non z ...

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Standard X

Mathematics

Section Formula

If x⃗ y...

Question

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 $Δ A B C$ 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
$(a - b) \to x + (b - c) \to y + (c - a) (\to x \times \to y) = 0$
As $\to x, \to y$ & $(\to x \times \to y)$ are non zero, non coplanar vectors,
then $a - b = b - c - a = 0$ $\Rightarrow$ $a = b = c$
Hence $Δ A B C$ is an equilateral triangle.
Hence, acute angled triangle.

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If →x & →y are two non collinear vectors and a, b, c represent the sides of a 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)=0 As →x,→y & (→x×→y) are non zero, non coplanar vectors, then a−b=b−c−a=0 ⇒ a=b=cHence ΔABC is an equilateral triangle. Hence, acute angled triangle.

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 $Δ A B C$ is