Find the lengths of the sides of the triangle PQR. Is it a right triangle? Is it an isosceles triangle? P(3, -2, -3), Q(7, 0, 1), R(1, 2, 1)

Question

Faiza Fuller · Accepted Answer

The distance between two points P1=(x1,y1,z1) and P2=(x2,y2,z2), denoted by d(P1,P2) is  d(P1,P2)=(x2−x1)2+(y2−y1)2+(z2−z1)2  The length of side width vetrices P(3,-2,-3) and Q(7,0,1) is  PQ=(3−7)2+(−2−0)2+(−3−1)2  PQ=(−4)2+(−2)2+(−4)2  PQ=16+4+16=36=6  The length of side with vetrices P(3,-2,-3) and R(1,2,1) is  PR=(3−1)2+(−2−2)2+(−3−1)2  PR=(2)2+(−4)2+(−4)2  PR=4+16+16=36=6  The length of side with vetrices Q(7,0,1) and R(1,2,1) is  QR=(7−1)2+(0−2)2+(1−1)2  QR=(6)2+(−2)2+(0)2  QR=36+4=40  This an isoceles triangle because two of its sides have equal lengths.  This is NOT a right triangle because sum of the squares of the smaller two sides is not equal to the square of the largest side  36+36≠40

Find the lengths of the sides of the triangle PQR. Is it a right triangle? Is it

Answered question

Answer & Explanation

New Questions in Integral Calculus