Trigonometry
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Two vectors a and b are given. Determine the dot products a ⋅ b and a ⋅ a:
a = i + 29j, b = 15i + j
a = 11i - 3j, b = -10i - 8j
a = -17i - 9j, b = -8i - 12j
a = i, b = 18j
Find a ⋅ (b + c) using the following vectors:
a = 9i - 4j, b = i + 5j, c = 8i + 3j
Find a ⋅ b + a ⋅ c using the following vectors:
Find (8a) ⋅ b using the following vectors:
a = 9i - 4j, b = i + 5j
Find 11(a ⋅ b) using the following vectors:
Calculate the angle between the two vectors a and b. Express the angle in degrees and round it to one decimal place.
a = 10i - 3j, b = 8i + 12j
a = -7i + 4j, b = 14i + -5j
a = 8i, b = 9i + 6j
Are the vectors a and b orthogonal?
a = 14i + 14j, b = 14i - 14j
a = 12i - 6j, b = 5i + 10j
a = 11i - 11j, b = -3i + 3j
a = 18i, b = -7i
a = 21i, b = -14j
Determine the projection of vector a onto vector b. Next, express vector a as vectors, a1 and a2, where a1 is parallel to vector b and a2 is perpendicular to vector b.
a = 6i -7j, b = i -4j
a = 11i -j, b = 3i +9j
a = 27i +2j, b = 81i +6j
Determine the specified scalar using the given information.
a = 3i -8j, b = 2i +6j and c = -8j
2a⋅(5b -3c)
Determine the specified vector using the given information.
proja(b +c)
For the vectors, a and b, determine the angle between both vectors.
a = 6cos(7π/3)i +6sin(7π/3)j, b = 12cos(5π/2)i +12sin(5π/2)j
Assess whether a and b are parallel, orthogonal, or do not possess either property.
a = 17i -24j, b = 85i -120j
a = 17i -24j, b = 85i +120j
a = 6i +11j, b = 5i -(30/11)j
It is given that a = 9i +7j, b = 2i -5j and 8i -3j, then determine a ⋅ (b + c).
For the given vectors a and b, compute the scalar product followed by determining the angle between the two vectors. Round the angle to the nearest tenth of a degree.
a = 3i +17j, b = 21i -2j
Find out if a and b are orthogonal by finding the dot product.
a = 13i -j, b = 3i +39j
a = 12i +5j, b = 2i +6j
For a = 6i +j and b = i -27j, determine the following scalar.
a⋅b
For a = 6i +j and b = i -27j, determine the following vector.
proj b a
Find the angle between the two vectors. Express the angle in degrees and round it to two decimal places.
〈7,12〉,〈−8,5〉〈7, 12〉, 〈-8, 5〉〈7,12〉,〈−8,5〉
〈15,0〉,〈5,3〉〈15, 0〉, 〈5, 3〉〈15,0〉,〈5,3〉
〈11,13〉,〈−11,14〉〈11, 13〉, 〈-11, 14〉〈11,13〉,〈−11,14〉
12i+13j,7j12\textbf{i} + 13\textbf{j}, 7\textbf{j}12i+13j,7j
17i+17j,−7i−7j17\textbf{i} + 17\textbf{j}, -7\textbf{i} - 7\textbf{j}17i+17j,−7i−7j
Are the following vectors orthogonal?
〈13,13〉,〈13,−13〉〈13, 13〉, 〈13, -13〉〈13,13〉,〈13,−13〉
17i−8j,−11i+417j\sqrt{17}\text{\textbf{i}}-8\text{\textbf{j}},-11\text{\textbf{i}}+4\sqrt{17}\text{\textbf{j}}17i−8j,−11i+417j
3i+67j,13i−7j3\text{\textbf{i}}+6\sqrt7\text{\textbf{j}},13\text{\textbf{i}}-\sqrt7\text{\textbf{j}}3i+67j,13i−7j