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What does the cross product give you in vector algebra?
The cross product in vector algebra gives you a new vector that is perpendicular to the two original vectors being multiplied.
What is meant by resolving a vector into components give an example?
Resolving a vector into components means breaking down the vector into perpendicular vectors that align along the coordinate axes. For example, a vector of magnitude 10 at an angle of 30 degrees with the x-axis can be resolved into x-component = 10cos(30) and y-component = 10sin(30) where cos(30) = √3/2 and sin(30) = 1/2.
What is the vector quantity for mass?
It isn't, because a mass can only be positive - there are no negative masses. Also mass is only referring to one thing and this doesn't give as much information as a vector quantity. Mass is scalar.
Can two vectors having different magnitude be combined to give a vector sum of zero?
Yes, two vectors with different magnitudes can be combined to give a vector sum of zero if they are in opposite directions and their magnitudes are appropriately chosen. The magnitude of one vector must be equal to the magnitude of the other vector, but in the opposite direction, to result in a vector sum of zero.
What does the addition of 2 vectors give you?
Adding two vectors results in a new vector that represents the combination of the two original vectors. The new vector is defined by finding the sum of the corresponding components of the two vectors.
What does the cross product give you in vector algebra?
The cross product in vector algebra gives you a new vector that is perpendicular to the two original vectors being multiplied.
What is the math defition for cross product?
the cross product is the multiplication of to vectors which results in another vector unlike the dot product witch equals a scalarthe you-tube videos below give more detailhttp://www.youtube.com/watch?v=KDHuWxy53uM&feature=youtube_gdatahttp://www.youtube.com/watch?v=E34CftP455k&feature=youtube_gdatahttp://www.youtube.com/watch?v=enr7JqvehJs&feature=youtube_gdata
Give some real examples for perpendicular lines?
Longitude and latitude lines are perpendicular to each other. Most road intersections in major cities are set up in a grid, making the cross streets perpendicular.
Why vector division is not possible?
In the case of the dot product, you would need to find a vector which, multiplied by another vector, gives a certain real number. This vector is not uniquely defined; several different vectors could be used to give the same result, even if the other vector is specified. For the other two common multiplications defined for vector, the inverse of multiplication, i.e. the division, can be clearly defined.
How do you show orthogonality of 3 unit vectors?
Showing that the scalar product between all pairs of them is equally zero.Two vector are orthogonal (or perpendicular) if the scalar product between them is zero. Lets see an example in 2D:If we have two vector, a = (a1, a2) and b = (b1,b2), ifa · b = sqrt(a1*b1 + a2*b2) = 0then a and b are orthogonal.To do the same with three vector (a, b, c) you have to show that all the combinations give zero, i.e.,a · b = a · c = b · c= 0(as the scalar product is commutative, you only need to probe this three cases).
What is the difference between finding the dot product and using scalar multiplication?
They give us different results. The dot product produces a number, while the scalar multiplication produces a vector.
What is meant by resolving a vector into components give an example?
Resolving a vector into components means breaking down the vector into perpendicular vectors that align along the coordinate axes. For example, a vector of magnitude 10 at an angle of 30 degrees with the x-axis can be resolved into x-component = 10cos(30) and y-component = 10sin(30) where cos(30) = √3/2 and sin(30) = 1/2.
When two vector combine form scalar quantity give example?
Two vector quantities can be combined into a scalar quantity because a vector lives in a vector space, which requires the existence of an operation called the dot product (also commonly known as the scalar product or inner product). The exact form of this operation depends on the type of vector space, and of course one can define other operations which map two vectors into a scalar. A commonly used definition is as follows: Imagine vector one contains these values (x1, x2, x3, x4) and vector two contains these values (y1, y2, y3, y4), the dot product would turn this into: x1*y1 + x2*y2 + x3*y3 + x4*y4 The dot product gives a measure of the angle between two vectors and is often used as such in for example mechanics.
Can you name any uses for dot product or cross product in video games?
The dot product can be used as a half space test. A half space test can be used to determine if an object, lets say a zombie, is in front of the player (or camera) or behind it. If my player's forward vector is P and the vector from the player to the zombie (zombie's position - player's position) is Z, then dotting P and Z would give me the angle between the two vectors. If the angle is positive our player is facing the zombie, otherwise the zombie is behind us (never turn your back on a zombie!).
Can you give me a sentence using the word perpendicular?
A flag pole is perpendicular to the ground.
What would be. perpendicular to y equals -3x-2?
y = 1/3x + cAlternate Answer:Any line with a slope of m is perpendicular to any line with a slope of 1/-m.Proof:We are working in the Euclidean space of R2. A vector fis orthogonal to another vector g, if their dot product is 0. The dot product is: fTg, or the sum of the product of the corresponding elements in each vector. I.e. fTg = f1*g1 + f2*g2 + f3g3 + ... + fngnFirst, Find the vector equation of a line centered at the origin:y = mxplug in x = 1y = mThis give you the direction vector m = (1, m)This in turn gives us the vector equation:r = mxr = (1, m)*xWe want to find some m', such that mTm'= 0Let m' = (c,d). We want to find c and d, such that 1c + md = 0c = -mdTherefore, m' = (-md,d), with d being any real number.Thus, the equationr' = m'*xis orthogonal/perpendicular to rFinally, we want to convert back to linear equations for both of our vector equations.We can express a vector equation of the form,s = (a, b)*xas a linear equation:a*y = b*xif we substitute r' for s, and m' for (a, b), we have:-m*d*y = d*xby isolating the y variable, we have:y = (1/-m)*xwhich is orthogonal to the line:y = m*xNow, we are almost done.For a line y = mx + b, we should note the angle it forms with another line, y = m'x + b' is always the same, for fixed m and m', and arbitrary b and b'. Thus the values of b and b' do not change the orthogonality of the system.QED.SO, for YOUR particular example, we would have y = -3x - 2 being orthogonal/perpendicular to ALL lines of the form y = (1/3)x + b, for any real number b.
What is a cross product and give an example?
It's part of a proportion. The cross products in a proportion are equal. example: 3/4 = 15/20 4x15 = 60 3x20 = 60
