Sure, here's a test for vectors:

Question 1: For the given vectors A = (3, 4) and B = (-2, 6), find the following:

a) The magnitude of vector A.
b) The direction of vector A in degrees.
c) The resultant of vector A and vector B.
d) The dot product of vector A and vector B.

Question 2: Given a vector C = (5, -3), find a vector D such that the resultant of vector C and vector D is equal to vector A.

Question 3: Two vectors P and Q have magnitudes 6 and 8 units, respectively. If the angle between them is 60 degrees, find the magnitude of their resultant.

Question 4: For the given vectors U = (2, -3) and V = (4, 5), find the angle between them in degrees.

Question 5: Given a vector W = (1, 2), find a unit vector in the direction of vector W.

Question 6: A force vector F has magnitude 10 N and is acting at an angle of 45 degrees with the horizontal axis. Find the horizontal and vertical components of the force vector.

Question 7: Two forces of magnitudes 5 N and 8 N act on an object. If the angle between them is 90 degrees, find the magnitude of the resultant force.

Question 8: A plane is flying at a speed of 400 km/h in the direction of 30 degrees east of north. Find the horizontal and vertical components of its velocity.

Question 9: A ship is moving with a velocity vector of magnitude 15 m/s in the direction of 45 degrees south of west. Find the horizontal and vertical components of its velocity.

Question 10: Two vectors X and Y have magnitudes 7 and 9 units, respectively. If the angle between them is 120 degrees, find the dot product of vector X and vector Y.

These questions cover various concepts related to vectors such as magnitude, direction, resultant, dot product, unit vectors, components, and angles between vectors. You can use these questions to assess your understanding of vectors and practice solving vector problems.

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