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If vector A is perpendicular to vector B and C then Vector A is parallel to?
Wiki User
∙ 11y ago
Vector A is parallel to the cross product of vectors B and C, and it is parallel to the axis that neither B or C lie along if the two other axes are defined as the axes that B and C lie along.
Wiki User
∙ 11y ago
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Is vector A parallel vector B given that vector A is equal to the zero vector and vector B is equal to the zero vector?
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.
If the component of vector A along the direction of vector B is zero. What can you conclude about these two vectors?
Their directions are perpendicular.
Can you add vector like scalars or not?
No. Because vectors have direction as well as magnitude, you must take the direction into account when you add them. Example: Vector A parallel to [0,0; 0,4] Vector B parallel to [0,0; 3,0] These vectors are at right angles to each other Vector A has a magnitude of 4, Vector B an magnitude of 3. A + B = has a magnitude of 5, parallel to [0,0;3,4]
How do you do cross products?
You need to know that the cross product of two vectors is a vector perpendicular to both vectors. It is defined only in 3 space. The formula to find the cross product of vector a (vector a=[a1,a2,a3]) and vector b (vector b=[b1,b2,b3]) is: vector a x vector b = [a2b3-a3b2,a3b1-a1b3,a1b2-a2b1]
Is it possible for vector A plus vector B to equal vector A - vector B?
It's impossible as the addition of two vectors is commutative i.e. A+B = B+A.For subtraction of two vectors, you have to subtract a vector B from vector A.The subtraction of the vector B from A is equivalent to the addition of (-B) with A, i.e. A-B = A+(-B).
Is vector A parallel vector B given that vector A is equal to the zero vector and vector B is equal to the zero vector?
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.
If the component of vector A along the direction of vector B is zero. What can you conclude about these two vectors?
Their directions are perpendicular.
Can you add vector like scalars or not?
No. Because vectors have direction as well as magnitude, you must take the direction into account when you add them. Example: Vector A parallel to [0,0; 0,4] Vector B parallel to [0,0; 3,0] These vectors are at right angles to each other Vector A has a magnitude of 4, Vector B an magnitude of 3. A + B = has a magnitude of 5, parallel to [0,0;3,4]
How do you do cross products?
You need to know that the cross product of two vectors is a vector perpendicular to both vectors. It is defined only in 3 space. The formula to find the cross product of vector a (vector a=[a1,a2,a3]) and vector b (vector b=[b1,b2,b3]) is: vector a x vector b = [a2b3-a3b2,a3b1-a1b3,a1b2-a2b1]
What is the angle between vector a and vector b when mode of vector a plus vector b is equal to mode of vector a minus vector b?
90 degrees
Is it possible for vector A plus vector B to equal vector A - vector B?
It's impossible as the addition of two vectors is commutative i.e. A+B = B+A.For subtraction of two vectors, you have to subtract a vector B from vector A.The subtraction of the vector B from A is equivalent to the addition of (-B) with A, i.e. A-B = A+(-B).
What happens if the electron enters the magnetic field parallel to B?
It continues in a straight line at a constant speed in the absence of any other field except the B vector field parallel to its velocity vector.
What can you say about two vectors if vector A vector B 0?
Depends on the situation. Vector A x Vector B= 0 when the sine of the angle between them is 0 Vector A . Vector B= 0 when the cosine of the angle between them is 0 Vector A + Vector B= 0 when Vectors A and B have equal magnitude but opposite direction.
What is the product of vector and scalar?
The scalar product of two perpendicular vectors is zero.In classical mechanics we define the scalar product between two vector a and b as:a · b = |a| |b| cos(alpha)where |a| is the modulus of vector a and alpha is the angle between vectors a and b.If two vectors are perpendicular, alpha equals 90º (or PI/2 rad) and cosine of alpha is, consequently, zero.So finally a · b = 0.
Cross product is not difine in two space why?
When performing the cross product of two vectors (vector A and vector B), one of the properites of the resultant vector C is that it is perpendicular to both vectors A & B. In two dimensional space, this is not possible, because the resultant vector will be perpendicular to the plane that A & B reside in. Using the (i,j,k) unit vector notation, you could add a 0*k to each vector when doing the cross product, and the resultant vector will have zeros for the i & jcomponents, and only have k components.Two vectors define a plane, and their cross product is always a vector along the normal to that plane, so the three vectors cannot lie in a 2D space which is a plane.
What is the dot product of two perpendicular vectors vector a and vector b respectively?
The dot product of two perpendicular vectors is 0. a⋅b = |ab|cos θ where: |a| = length of vector a |b| = length of vector b θ = the angle between the vectors. If the vectors are perpendicular, θ = π/2 radians → cos θ = cos(π/2) = 0 → a⋅b = |a| × |b| × 0 = 0 ----------------------------------------------------------------------------- The dot product can also be calculated for vectors of n dimensions as the sum of the products of the corresponding elements: a = (a1, a2, ..., an) b = (b1, b2, ..., bn) a⋅b = Σ ar × br for r = 1, 2 , ..., n With perpendicular vectors this sum is zero,
How do you find a normal vector?
A normal vector is a vector that is perpendicular or orthogonal to another vector. That means the angle between them is 90 degrees which also means their dot product if zero. I will denote (a,b) to mean the vector from (0,0) to (a,b) So let' look at the case of a vector in R2 first. To make it general, call the vector, V=(a,b) and to find a vector perpendicular to v, i.e a normal vector, which we call (c,d) we need ac+bd=0 So say (a,b)=(1,0), then (c,d) could equal (0,1) since their dot product is 0 Now say (a,b)=(1,1) we need c=-d so there are an infinite number of vectors that work, say (2,-2) In fact when we had (1,0) we could have pick the vector (0,100) and it is also normal So there is always an infinite number of vectors normal to any other vector. We use the term normal because the vector is perpendicular to a surface. so now we could find a vector in Rn normal to any other. There is another way to do this using the cross product. Given two vectors in a plane, their cross product is a vector normal to that plane. Which one to use? Depends on the context and sometimes both can be used!
