# Can the intersection of two planes be a line?

## Can the intersection of two planes be a line?

Two intersecting planes always form a line If two planes intersect each other, the intersection will always be a line.

Can the intersection of a plane and a line segment be a line segment?

Represent the plane by the equation ax+by+cz+d=0 and plug the coordinates of the end points of the line segment into the left-hand side. If the resulting values have opposite signs, then the segment intersects the plane. If you get zero for either endpoint, then that point of course lies on the plane.

### Do any two planes intersect explain?

Explanation: In 3 dimensional Euclidean space, two planes may intersect as follows: If one plane is identical to the other except translated by some vector not in the plane, then the two planes do not intersect ” they are parallel. If the two planes coincide, then they intersect in a plane.

Where do two planes intersect in a line?

The intersection of two planes is always a line If two planes intersect each other, the intersection will always be a line. where r 0 r_0 r0​ is a point on the line and v is the vector result of the cross product of the normal vectors of the two planes.

## Do 2 points always create a line?

ANSWER: Never; Postulate 2.1 states through any two points, there is exactly one line. 26. If points M, N, and P lie in plane X, then they are collinear.

Can three planes intersect at one point?

all three planes form a cluster of planes intersecting in one common line (a sheaf), all three planes form a prism, the three planes intersect in a single point.

### How many ways can 3 planes intersect?

Intersection of Three Planes

Can planes intersect at a point?

They cannot intersect at only one point because planes are infinite. Furthermore, they cannot intersect over more than one line because planes are flat. One way to think about planes is to try to use sheets of paper, and observe that the intersection of two sheets would only happen at one line.

## Do rays intersect?

8 Answers. Given: two rays a, b with starting points (origin vectors) as, bs, and direction vectors ad, bd. If this equation system has a solution for u>=0 and v>=0 (the positive direction is what makes them rays), the rays intersect

Can a ray be called SR and RS?

Ray SR can not be called RS because rays only go in one direction is the ray were RS it would be going the opposite direction or ray SR

### What is an opposite Ray?

Opposite rays are two rays that both start from a common point and go off in exactly opposite directions. Because of this the two rays (QA and QB in the figure above) form a single straight line through the common endpoint Q. When the two rays are opposite, the points A,Q and B are collinear.

What is the difference between Ray AB and Ray ba?

No, Ray AB and Ray BA are not same. Ray: It has one initial point and it goes upto infinity. Initial Point of Ray AB is A and that of ray BA is B. So these rays are moving in opposite directions to each other

## How do you identify a ray?

In naming a ray, we always begin with the letter of the endpoint (where the ray starts) followed by another point on the ray in the direction it travels. Since the vertex of the angle is the endpoint of each ray and our vertex is , each of our rays must begin with .

How do you write a Ray?

A segment is named by its two endpoints, for example, ¯AB . A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray. A ray is named using its endpoint first, and then any other point on the ray (for example, ‘BA ).

### Is AB the same as BA?

In general, AB = BA, even if A and B are both square.

Is AB equal to BA in sets?

We can find the DIFFERENCE of two sets . A-B is the set of all elements that are in A but NOT in B, and B-A is the set of all elements that are in B but NOT in A. Notice that A-B is always a subset of A and B-A is always a subset of B.

## Is a * b B * A?

If and are numbers, then yes. Well, if A and B are numbers,yes A*B=B*A is always true.

What is equivalent to AB?

### Is BA a Ab?

Bachelor of Arts (BA or AB; from the Latin baccalaureus artium or artium baccalaureus) is the holder of a bachelor’s degree awarded for an undergraduate program in the arts and sciences. …

What is A /( B C?

In a/(b/c) b/c is denominator. So a/(b/c) = (a×c)/ b. Eg 3/(4/5)= (3×5)/4.

## What does AB mean in maths?

Common Symbols Used in Geometry

What does B stand for?

B is a letter, yes, but it’s also a shortening of several words: brother, babe, bae, boo … you get the point.

### What does B stand for math?

bisect bisector Base

What is AxB algebra?

AxB consists of every possible ordered pair of elements, such that each pair has an element of A as its first number, and an element of B as its second number.

## What does AxB mean?

Cartesian Product

Is AxB a BxA?

Cross products produce a third orthogonal(perpendicular) vector to A and B. Using the right hand rule for cross products, you can see AxB and BxA will always be pointing in opposite directions. That’s why AxB = -(BxA) is always true but AxB =BxA is never true.

### How is AxB calculated?

Magnitude: |AxB| = A B sinθ. Just like the dot product, θ is the angle between the vectors A and B when they are drawn tail-to-tail. Direction: The vector AxB is perpendicular to the plane formed by A and B. Use the right-hand-rule (RHR) to find out whether it is pointing into or out of the plane.

What is the value of I cross I?

The value of i cap × i cap is equal to 0. Hence, the value of i cap × i cap is equal to 0

## What is the cross product of i and j?

We can use these properties, along with the cross product of the standard unit vectors, to write the formula for the cross product in terms of components. Since we know that i×i=0=j×j and that i×j=k=’j×i, this quickly simplifies to a×b=(a1b2’a2b1)k=|a1a2b1b2|k.

What is a dot B?

The dot product of two Euclidean vectors a and b is defined by. where θ is the angle between a and b. In particular, if the vectors a and b are orthogonal (i.e., their angle is π / 2 or 90°), then , which implies that. At the other extreme, if they are codirectional, then the angle between them is zero with and.

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