Consider two vectors A and B, expressed in unit vector notation as A = a1i + a2j and B = b1i + b2j. Enter an expression for the difference vector A - B in terms of quantities shown in the expressions and an expression for the square of the magnitude of the sum vector |A + B| in terms of quantities shown in the expressions.

A vector with magnitude 6, points in a direction counterclockwise from the positive x-axis. Write the vector in component form. Give each value accurate to at least 1 decimal place.

A vector has the components Ax=22mAx=22m and Ay=16mAy=16m. a) What is the magnitude of this vector? Express your answer to two significant figures and include appropriate units.   b) What angle does this vector make with the positive x axis? Express your answer to two significant figures and include appropriate units.

Problem 2: A vector has x and y components 7.8 and 9.9 respectively. Part (a) What is the magnitude of this vector? Numeric : Anumeric value is expected and not an expression. r = Part (b) What is the direction of this vector in degrees? Numeric : A numeric value is expected and not an expression. 0 =

The displacement vectors A and B shown in the figure below both have magnitudes of 2.05 m. The direction of vector A is 0 = 44.0°. (a) Find A + B graphically. magnitude direction m (b) Find A - B graphically. magnitude direction (c) Find B - A graphically. magnitude direction counterclockwise from the +x axis m (d) Find A 2B graphically. magnitude direction counterclockwise from the +x axis m counterclockwise from the +x axis m o counterclockwise from the +x axis

Two vectors A and B are shown in the figure. Vector A has a magnitude of r = 24.5 and an angle of 0A = 25.9°. Vector B has a magnitude of rB = 44.5 and an angle of 0B = 61.5°. The figure is not to scale. Express each vector in the figure using ijk unit vector notation, A = Axi + Ayj B = B₂i + B₂j where Ax, Ay, Bx, and By are the calculated values of the x- and y-components of vectors A and B, respectively. A = B = B TB OB TA 0

a displacement vector points in a direction of θ= 33 degrees left of the positive y axis . the magnitude of this vector is D= 180 m. enter an expression for the x component vector Dx in terms of D,θ, and the unit vectors i and j.

Vector Ä has a magnitude of 10 units and a direction angle of 14° measured counterclockwise from the positive r-axis. Vector B has the same r-component as Ä, but its y-component is 3 times larger. What is the magnitude and direction angle of vector B?

The vector A has a magnitude of 4.0 meters and points in the -x direction. The vector B has a magnitude of 3.0 meters and points in the +y direction. Vector C is defined so that C - A + B = 0. What is the magnitude and direction of vector C? Give your answers to 2 significant figures.

A vector has an x-component of 23.5 units and a y-component of 31.5 units. Find the magnitude and direction of the vector. magnitude: direction: (counterclockwise from the +x-axis)