Respuesta :
Yes. It is a right-angled triangle.
The vectors that make up the triangle must first be located. The vertices are subtracted to achieve this.
QP=(2,0,-4)-(1,-3,-2)=(1,3,-2)
PR=(1,-3,-2)-(6,-2,-5)=(-5,-1,3)
RQ=(6,-2,-5)-(2,0,-4)=(4,-2,-1)
QP.PR = (1, 3, -2).(-5, -1, 3) = -5-3-6= -14
PR.RQ = (-5, -1, 3).(4, -2, -1) = -20+2-3 = -21
RQ.QP = (4, -2, -1).(1, 3, -2) = 4-6+2 = 0
Calculate the dot products to see if these vectors are perpendicular now.
They are perpendicular if the dot product of two vectors equals zero. As you can see, RQ.QP is zero in your triangle, which supports this. Consequently, a right-angled triangle results.
What is a dot-product?
The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of numbers of equal length (often coordinate vectors) and outputs a single number. The dot product of two vectors' Cartesian coordinates is frequently used in Euclidean geometry. Although other inner products can be defined in Euclidean space, it is frequently referred to as the inner product (or, less frequently, projection product) of Euclidean space (see Inner product space for more).
The sum of the products of the matching entries of the two number sequences is the dot product, according to algebra. B, it is the result of adding the cosine of the angle between the two vectors and the Euclidean magnitudes of the two vectors.
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