For the vectors given in the following figure, use a graphical method to find the following resultants: C→ − 2 D→ + 3 F→

Vector A→, which is directed along an x axis, is to be added to vector B→, which has a magnitude of 9.30 m. The sum is a third vector that is directed along the y axis, with a magnitude that is 5.10 times that of A→. What is the magnitude of A→?

The figure shows three vectors. Vector A→ has a length of 31.0, vector B→ has a length of 67.0, and vector  C→ has a length of 22.0. Find each magnitude and direction.   |A→×B→|= ?     direction: ?   |C→×B→|= ?

The two vectors a→ and b→ in the figure have equal magnitudes of 10.2 m and the angles are θ1 = 30° and θ2 = 101°. Find (a) the x component and (b) the y component of their vector sum r→, (c) the magnitude of r→, and (d) the angle r→ makes with the positive direction of the x axis.

Two vectors A→ and  B→ are at right angles to each other. The magnitude of  A→ is 1.00. What should be the length of  B→ so that the magnitude of their vector sum is 2.00?

Use the definition of scalar product, a = ab cos 0, and the fact that a . the two vectors given by a = 3.01 +3.0 + 3.0k and b Number i Units = axbx + ab + a₂b₂ to calculate the angle between 4.0î + 9.0ĵ + 7.0k. =

The following vectors are defined (e, ey, ē,) are unit vectors of an orthogonal coordinate system): d = 2ẻ, + ẻ, - 3ể,z b = ëz – 6ẽ, – ẻ, c = 2e, + 3ẻ, + 4ẻ, Determine the following: (1) Scalar product of vectors à and b; (2) Scalar product of vectors b and b; (3) Magnitude of vector b ; (4) Cross product of ä and ä ; (5) Cross product of a and b.

For the vectors in the figure, with a = 8.0, b = 6.0, and c = 10  what are the magnitude and the direction b×c?

Note: Please provide a simple and step-by-step solution.