When two vectors A and B are added then maximum value of resultant is?
Answer. R is maximum when Cos ( A, B) = +1 ie angle between vectors A and B is zero ie vectors A and B are parallel to each other. The resultant of two vector is minimum when both vectors are equal and in opposite direction i.e. the angle between the vector is 180 degrees.
When two vectors A and B are at an angle?
Vectors and the Parallelogram Rule When two vectors A and B are at an angle to each other, they add to produce the resultant C by the parallelogram rule. Note that C is the diagonal of a parallelogram where A and B are adjacent sides.
What angle is the vector +B?
So, the angle between two vectors a and b is θ = 64.94º .
What is angle between vector a B and AB?
b =0. ∴a ⊥b. ∴θ=90∘ Hence, Angle btween two vector is 90o. Answer verified by Toppr.
What is the vector equation of XY plane?
That is their dot product with XY plane is equal to zero. So the equation of the plane is →r. ∧k=0 or we know that a point lying on this plane has z coordinate is 0. So the equation can also be written as →r=a∧i+b∧j.
Is a vector a line?
Vectors are not lines and they have a very different function than lines. A vector is a direction and a magnitude, that’s it. A line, of course, has direction and magnitude, but it also has LOCATION. A vector can be anywhere, but a line exists within space.
What is the direction vector of a line?
We begin by finding two points that lie on the line. Choose x = 0 and find the corresponding y value. Find a vector that joins these two points and can call it . has the same direction as the line and is called a direction vector. If we rotate the vector by 90º we get a vector that is perpendicular to the line.
What is Cartesian equation of a line?
Equation of a line is defined as y= mx+c, where c is the y-intercept and m is the slope. Vectors can be defined as a quantity possessing both direction and magnitude. Position vectors simply denote the position or location of a point in the three-dimensional Cartesian system with respect to a reference origin.
What is a Cartesian vector?
The vector , being the sum of the vectors and , is therefore. This formula, which expresses in terms of i, j, k, x, y and z, is called the Cartesian representation of the vector in three dimensions. We call x, y and z the components of. along the OX, OY and OZ axes respectively.
What is the difference between vector and Cartesian form?
1 Answer. Cartesian coordinates are one way to write down vectors as a bunch of numbers. Cartesian coordinates are a way to write down a vector by expressing every vector as a linear combination of basis vectors.
What is Cartesian theory?
Cartesians adopted an ontological dualism of two finite substances, mind (spirit or soul) and matter. The essence of mind is self-conscious thinking; the essence of matter is extension in three dimensions. God is a third, infinite substance, whose essence is necessary existence.
Is Cartesian form same as rectangular form?
Cartesian form and rectangular form are two different names for the same system. A complex number “z = a + bi” form is called cartesian form or rectangular form.
What is Cartesian standard form?
The standard form of a line in the Cartesian plane is given by. for real numbers . This form can be derived from any of the other forms (point-slope form, slope-intercept form, etc.), but can be seen most intuitively when starting from intercept form.
What is the Cartesian form of?
A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.
How do you find the Cartesian form?
A cartesian equation of a curve is simply finding the single equation of this curve in a standard form where xs and ys are the only variables. To find this equation, you need to solve the parametric equations simultaneously: If y = 4t, then divide both sides by 4 to find (1/4)y = t.
What is Cartesian form and polar form?
Summary. To convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y) : x = r × cos( θ ) y = r × sin( θ )