Q: A vector a is along the positive z axis and it's vector product with another vector b is zero then vector b could be?

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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.

Any vector can be "decomposed" into components along any two non-parallel directions. In particular, a vector may be decomposed along a pair (more in higher dimensional spaces) of orthogonal directions. Orthogonal means at right angles and so you have the original vector split up into components that are at right angles to each other - for example, along the x-axis and the y-axis. These components are the rectangular components of the original vector. The reason for doing this is that vectors acting at right angles to one another do not affect one another.

No. Cos theta (Cos θ) is a trigonometric function. A vector is any physical quantity which has both magnitude and direction. For example, Displacement. Displacement has a magnitude like 240m or 0 or 13 m, etc. It also depends on the direction. If an object moves along the positive direction of x-axis, then the displacement will have a positive sign and if it moves along the negative direction of x-axis, then displacement will be negative. Thus, it has both direction and magnitude and so is a vector. Cos theta is a trigonometric function, strictly speaking.

The x component of V1 is -6.6 the y component of V1 is 0.

When the arrow representing the vector would point toward negative x.

Related questions

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.

You should express a vector along the x-axis as negative when it points in the negative x-direction relative to a chosen positive direction. This convention helps maintain consistency with vector addition and trigonometric methods.

Yes. The "direction" of the vector is along the axis of rotation.Yes. The "direction" of the vector is along the axis of rotation.Yes. The "direction" of the vector is along the axis of rotation.Yes. The "direction" of the vector is along the axis of rotation.

[abc][k] [10] [a,-b] [01] [-c,k]

A tangent of the vector is the projection of a vector along the axes of a coordinate system.

If one component of vector A is zero along the direction of vector B, it means the two vectors are orthogonal or perpendicular to each other. Their directions would be such that they are at a right angle to each other.

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.

Any vector can be "decomposed" into components along any two non-parallel directions. In particular, a vector may be decomposed along a pair (more in higher dimensional spaces) of orthogonal directions. Orthogonal means at right angles and so you have the original vector split up into components that are at right angles to each other - for example, along the x-axis and the y-axis. These components are the rectangular components of the original vector. The reason for doing this is that vectors acting at right angles to one another do not affect one another.

To find the direction of a vector, you can use the formula: θ = tan^(-1) (y/x), where θ is the angle of the vector with the positive x-axis, and (x, y) are the components of the vector along the x and y axes, respectively.

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.

"Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another." (from Wikipedia)

Translation along a vector involves moving an object in a specific direction by a specified distance based on the properties of the vector. This operation involves shifting the object without rotating or changing its orientation, following the direction and magnitude of the vector.