Question

英文数学题！！谢谢！！

1.Find the angle between the line joining (1,3,-2)and(2,5,-1)and the line joining(-1,4,3)to(3,2,1).
2.ABCD is the base of a square pyramid of side 2 units, and V is the vertex. The pyramid is symmetrical, and of height 4 units. Calculate the acute angle between AV and BC, giving answer correct to 1 decimal place.

Answer 1

.Find the angle between the line joining (1,3,-2)and(2,5,-1)and the line joining(-1,4,3)to(3,2,1).
2.ABCD is the base of a square pyramid of side 2 units, and V is the vertex. The pyramid is symmetrical, and of height 4 units. Calculate the acute angle between AV and BC, giving answer correct to 1 decimal place.

Answer 2

2、AV and BC are skew lines, so they don't meet at an angle. Therefore, I'll assume you're talking about vectors.

Then we can label the points:
A(0,0,0)
B(2,0,0)
C(2,2,0)
D(0,2,0)
V(1,1,4)

with vectors:
AV = (1,1,4)
BC = (0,2,0)

|AV| = 3sqrt(2)
|BC| = 2
<AV, BC> = 2

2 = 2 * (3sqrt(2)) * cos(x)
cos(x) = sqrt(2) / 6
x = cos^-1(sqrt(2) / 6) = 76.37 degrees.

Answer 3

不太懂

Answer 4

哦~~~~看不懂