Given plane Π : f(x,y,z) = 4x+3y-z = -1
Need to find point P on Π that is closest to the origin O=(0,0,0).
Solution:
First step: check if O is on the plane Π : f(0,0,0)=0 ≠ -1 => O is not on Π
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e.
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane Π , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane Π
Answer: P(-2/13, -3/26, 1/26) is the point on Π closest to the origin.
Answer:
3 ≥ x
Step-by-step explanation:
Answer with Step-by-step explanation:
We are given that:
tanA = 0.45
tanA= 
= 
⇒ =0.45
⇒ 
=
⇒ =
⇒ AC= 20
Hence, by pythagoras theorem
AB²=AC²+BC²
AB²=20²+9²
AB²=481
⇒ AB=21.9 units
Hence, the approximate length of AB is:
22 units
Answer:
Minor arcs are linked with smaller than half of a rotation, so minor arcs are linked with angles that are less than 180°. Major arcs are linked with more than half of a rotation, so major arcs are linked with angles greated than 180°.
Step-by-step explanation:
Answer:the area is 28.27
Step-by-step explanation:
im just that good
