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A vector, starting at the origin and going to point (-2,0):
Since there is no y-component, the magnitude is the absolute value of the x component
magnitude = 2
magnitude of a vector = sqrt( X2 + Y2) = sqrt ((-2)2 + 02) = sqrt(4) = 2
where X & Y are the x-component & y-component of the vector.
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How can you find a unit vector in the same direction as the given vector?
Divide the vector by it's length (magnitude).
Why is it necessary to use the trig function cosine when working with vectors?
The cosine function is used to determine the x component of the vector. The sine function is used to determine the y component. Consider a vector drawn on an x-y plane with its initial point at (0,0). If L is the magnitude of the vector and theta is the angle from the positive x axis to the vector, then the x component of the vector is L * cos(theta) and the y component is L * sin(theta).
Prove that a constant vector always has a perpendicular derivative?
A dot A = A2 do a derivative of both sides derivative (A) dot A + A dot derivative(A) =0 2(derivative (A) dot A)=0 (derivative (A) dot A)=0 A * derivative (A) * cos (theta) =0 => theta =90 A and derivative (A) are perpendicular
How do you solve equation by completing the square p2-2p-3 equals 0?
p^2 - 2p - 3 = 0 p^2 - 2p = 3 halve the linear term (-2), square it and add it to both sides p^2 - 2p + 1 = 3 + 1 factor left, gather terms right (p - 1)^2 = 4 (p - 1)^2 - 4 = 0 (1,-4) are the vector points of this parabola You can factor to solve for p (p + 1)(P - 3) p = - 1 p = 3
Solve 2x squared - 6x plus 4 equals 0?
2x2 - 6x + 4 = 0 2(x2 - 3x + 2) = 0 2(x - 1)(x - 2) = 0 x - 1 = 0 and x - 2 = 0 So, x = 1 and x = 2.
Which vector have no magnitude?
The zero vector has no magnitude. v= Io + Jo + k0 has no magnirude |V|= sqroot(o^2 + 0^2 + 0^2)=0.
Suppose vector equation A plus B equals 0.how does the magnitude of B compare to that of A?
If vector equation A + B = 0, it means that vector B is equal in magnitude but opposite in direction to vector A. Therefore, the magnitude of vector B is equal to the magnitude of vector A.
Can a vector have a component equal to zero and still have a nonzero magnitude?
Yes. For instance, the 2-dimensional vector (1,0) has length sqrt(1+0) = 1 A vector only has zero magnitude when all its components are 0.
When do you get a magnitude of 0 in vector?
The magnitude of a vector is 0 if the magnitude is given to be 0.The magnitude of the resultant of several vectors in n-dimensional space is 0 if and only if the components of the vectors sum to 0 in each of a sewt of n orthogonal directions.
Can a vector with the magnitude of 2 be added to a vector with a magnitude of 3?
5
Can a a vector with 0 magnitude have a nonzero component?
No.
Find a vecot equivalent to the vector PQ with its initial point at the origin and find the magnitude of the vector P equals -4 -3 Q equals -2 2?
vector PQ where P(-4, -3) and Q(-2, 2) equivalent vector P'Q' where P'(0, 0) and Q'(2, 5) the magnitude doesn't change so we can compute |P'Q'| = √(22 + 52) = √29
Why null vector has a direction as it has magnitude 0?
The null vector is a special case where both magnitude and direction are undefined. This vector represents a point in space, rather than a physical quantity with magnitude and direction.
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 a unit vector?
It is a vector whose magnitude is 1.It is a vector whose magnitude is 1.It is a vector whose magnitude is 1.It is a vector whose magnitude is 1.
Can a vector have zero magnitude if one of its components is nonzero?
A vector comprises its components, which are orthogonal. If just one of them has magnitude and direction, then the resultant vector has magnitude and direction. Example:- If A is a vector and Ax is zero and Ay is non-zero then, A=Ax+Ay A=0+Ay A=Ay
Can a component of a vector be greater than the vector's magnitude?
No. If the vector is 2D then it's magnitude is (x^2+y^2)^0.5 where x and y are the components and ^0.5 means take the square root. In 3D this becomes (x^2+y^2+z^2)^0.5 etc. Thus the magnitude is always at least as big as one of the components. Here's an example of a 3D vector: (3,4,5) |(3,4,5)|=(3^2+4^2+5^2)^0.5=(9+16+25)^0.5=50^0.5=7.07... If y and z were 0: (3,0,0) |(3,0,0)|=(3^2+0^2+0^2)^0.5=(9+0+0)^0.5=9^0.5=3 ie the magnitude is the same size as x. You can also consider this geometrically. A vector is an arrow and the magnitude represents the length of the arrow. Vector addition is the 'adding' of these arrows so (3,4,5)=(3,0,0)+(0,4,0)+(0,0,5). Clearly the length of an arrow built of three smaller ones can't be less than any one of them.
