Dot Product Practice Problems

Two vectors a and b are given. Determine the dot products a ⋅ b and a ⋅ a:

a = i + 29j, b = 15i + j

Two vectors a and b are given. Determine the dot products a ⋅ b and a ⋅ a:

a = 11i - 3j, b = -10i - 8j

Two vectors a and b are given. Determine the dot products a ⋅ b and a ⋅ a:

a = -17i - 9j, b = -8i - 12j

Two vectors a and b are given. Determine the dot products a ⋅ b and a ⋅ a:

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:

a = 9i - 4j, b = i + 5j, c = 8i + 3j

Find (8a) ⋅ b using the following vectors:

a = 9i - 4j, b = i + 5j

Find 11(a ⋅ b) using the following vectors:

a = 9i - 4j, b = i + 5j

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

Calculate the angle between the two vectors a and b. Express the angle in degrees and round it to one decimal place.

a = -7i + 4j, b = 14i + -5j

Calculate the angle between the two vectors a and b. Express the angle in degrees and round it to one decimal place.

a = 8i, b = 9i + 6j

Are the vectors a and b orthogonal?

a = 14i + 14j, b = 14i - 14j

Are the vectors a and b orthogonal?

a = 12i - 6j, b = 5i + 10j

Are the vectors a and b orthogonal?

a = 11i - 11j, b = -3i + 3j

Are the vectors a and b orthogonal?

a = 18i, b = -7i

Are the vectors a and b orthogonal?

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

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 = 11i -j, b = 3i +9j

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 = 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. 

a = 3i -8j, b = 2i +6j and c = -8j

proj_a(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

Assess whether a and b are parallel, orthogonal, or do not possess either property. 

a = 17i -24j, b = 85i +120j

Assess whether a and b are parallel, orthogonal, or do not possess either property. 

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

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 = 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.

$〈7, 12〉, 〈-8, 5〉$

Find the angle between the two vectors. Express the angle in degrees and round it to two decimal places.

$〈15, 0〉, 〈5, 3〉$

Find the angle between the two vectors. Express the angle in degrees and round it to two decimal places.

$〈11, 13〉, 〈-11, 14〉$

Find the angle between the two vectors. Express the angle in degrees and round it to two decimal places.

$12\textbf{i} + 13\textbf{j}, 7\textbf{j}$

Find the angle between the two vectors. Express the angle in degrees and round it to two decimal places.

$17\textbf{i} + 17\textbf{j}, -7\textbf{i} - 7\textbf{j}$

Are the following vectors orthogonal?

$〈13, 13〉, 〈13, -13〉$

Are the following vectors orthogonal?

$\sqrt{17}\text{\textbf{i}}-8\text{\textbf{j}},-11\text{\textbf{i}}+4\sqrt{17}\text{\textbf{j}}$

Are the following vectors orthogonal?

$3\text{\textbf{i}}+6\sqrt7\text{\textbf{j}},13\text{\textbf{i}}-\sqrt7\text{\textbf{j}}$