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What is the expression for the unit vector r hat in spherical coordinates?
The expression for the unit vector r hat in spherical coordinates is r hat sin(theta)cos(phi) i sin(theta)sin(phi) j cos(theta) k.
How a vector can be express in term of its rectangular component?
A vector can be represented in terms of its rectangular components for example : V= Ix + Jy + Kz I, J and K are the rectangular vector direction components and x, y and z are the scalar measures along the components.
What is the difference between a unit vector and a unit basis vector?
A unit vector is a vector with a magnitude of 1, while a unit basis vector is a vector that is part of a set of vectors that form a basis for a vector space and has a magnitude of 1.
Which are the three vectors that act along the mutually perpendicular direction?
The three vectors that act along mutually perpendicular directions are the unit vectors in the x, y, and z directions, namely, i, j, and k. These vectors form the basis for three-dimensional space and are commonly used in physics and mathematics.
If a vector quantity is divided by its magnitude the vector obtained is called?
The vector obtained by dividing a vector by its magnitude is called a unit vector. Unit vectors have a magnitude of 1 and represent only the direction of the original vector.
What is the expression for the unit vector r hat in spherical coordinates?
The expression for the unit vector r hat in spherical coordinates is r hat sin(theta)cos(phi) i sin(theta)sin(phi) j cos(theta) k.
What is the vector equation for the x axis?
ki where i is the unit horizontal vector, and k is any number.
What is the letter j in maths?
J can be anything u want it to be...but typically j is a vector along y axis ( for example a point has vector equation i+3j+4k this mean that the point is 1 unit along x -axis (i) , 3 units along y-axis (j) , and 4 units along z-axis (k). )
Center of curvature in differential calculus?
Center of curvature = r(t) + (1/k)(unit inward Normal) k = curvature Unit inward normal = vector perpendicular to unit tangent r(t) = position vector
Can you add three unit vectors to get a unit vector does your answer change if two unit vectors are along the coordinate axes?
Yes., and their being along the coordinate axes does not change the answer.Consider the vectors: i, -i and j where i is the unit vector along the x axis and j along the y axis. The resultant of the three is j.
What you the math terms for j?
A unit vector in the positive direction of the y-axis.
What is a plus b and a - b and c given a - b plus c equals 0 given vector a equals 4.0 i - 3.0 j plus 1.0 k and vector b equals -1.0 i plus 1.0 j plus 4.0 k?
a = 4.0 i - 3.0 j + 1.0 k b = -1.0 i + 1.0 j + 4.0 k → a + b = (4.0 + -1.0) i + (-3.0 + 1.0) j + (1.0 + 4.0) k = 3.0 i - 2.0 j + 5.0 k → a - b = (4.0 - -1.0) i + (-3.0 - 1.0) j + (1.0 - 4.0) k = 5.0 i - 4.0 j - 3.0 k → a - b + c = 0 → c = -(a - b) = -5.0 i + 4.0 j + 3.0 k So that a - b + c = (5.0 - 5.0) i + (-4.0 + 4.0) j + (-3.0 + 3.0) k = 0 i + 0 j + 0 k = 0.
How a vector can be express in term of its rectangular component?
A vector can be represented in terms of its rectangular components for example : V= Ix + Jy + Kz I, J and K are the rectangular vector direction components and x, y and z are the scalar measures along the components.
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.
Can a vector be represented in terms of unit vector?
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
What is the difference between a unit vector and a unit basis vector?
A unit vector is a vector with a magnitude of 1, while a unit basis vector is a vector that is part of a set of vectors that form a basis for a vector space and has a magnitude of 1.
Find the scalar multiple of a vector?
by this do you means*Vwhere s is the scalar and V is the vector?if V = ai + bj + ck thens*V = (s*a)i + (s*b)j + (s*c)kwhere i, j and k are the unit vectors and a,b and c are constantsEssentially you just multiply each part of the vector by the scalar
