utefdxd的部落格

標題:

Maths Vector problem

發問:

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The vertices A,B, and C of a triangle are given by the points (.1, 0, 2), (0, 1, 0), and (1,.1, 0), respectively. Find point D so that the figure ABCD forms a plane parallelogram. 我本書有答案，但係我想要STEPS，THX PS ANS. (0,?2, 2) or (2, 0,?2).

最佳解答:

Let the coordinates of D be (x, y, z) vector AB = (0i + 1j + 0k) - (-1i - 0j - 2k) = i + j - 2k vector CD = (xi + yj + zk) - (1i - 1j - 0k) = (x - 1)i + (y + 1)j + zk vector DC = - vector CD = (1 - x)i - (y + 1)j - zk Since ABCD forms a parallelogram, AB = CD and AB // CD (property of parallelogram). Thus, vector AB = vector CD or vector AB = vector DC. i + j - 2k = (x - 1)i + (y + 1)j + zk or i + j - 2k = (1 - x)i - (y + 1)j - zk x = 2, y = 0, z = -2 or x = 0, y = -2, z = 2 Therefore, the coordinates of D are (2, 0, -2) or (0, -2, 2)

其他解答:

我應為從一個三角形做出一個平行四邊形應該有三個答案： AB 變成平行四邊形的對角線。 BC 變成平行四邊形的對角線。 CA 變成平行四邊形的對角線。|||||The vertices A，B，and C of a triangle are given by the points (－1，0，2)，(0，1，0)，and (1，－1，0)，respectively．Find point D so that the figureABCD forms a plane parallelogram Sol 設D(a，b，c) (1) 平行四邊形ABCD a－1=－1－0，a=0 b+1=0－1，b=－2 c－0=2－0，c=2 D(0，－2，2) (2) 平行四邊形ABDC a－1=０＋１，a＝2 b+1=1－0，b=0 c－0=0－2，c=－2 D(2，０，－2) 2013-02-21 13:38:22 補充： (3) 平行四邊形ACBD a－0=－1－１，a=－2 b－1=0+1，b=2 c－0=2－0，c=2 D(－2，2，2)