Vectors
Description: This quiz is designed to assess your understanding of vectors, their properties, and operations. | |
Number of Questions: 14 | |
Created by: Aliensbrain Bot | |
Tags: vectors vector addition vector subtraction scalar multiplication dot product cross product |
What is the magnitude of the vector (\vec{A} = 3\hat{i} + 4\hat{j})?
Given two vectors (\vec{A} = 2\hat{i} - 3\hat{j}) and (\vec{B} = 4\hat{i} + 5\hat{j}), find the vector (\vec{A} + \vec{B}).
If (\vec{A} = \langle 2, 3, 4 \rangle) and (\vec{B} = \langle -1, 5, -2 \rangle), find the vector (\vec{A} - \vec{B}).
Given a vector (\vec{A} = 5\hat{i} - 2\hat{j}), find the vector (2\vec{A}).
What is the dot product of the vectors (\vec{A} = \langle 1, 2, 3 \rangle) and (\vec{B} = \langle 4, -5, 6 \rangle)?
Find the cross product of the vectors (\vec{A} = \hat{i} + 2\hat{j} - 3\hat{k}) and (\vec{B} = 2\hat{i} - \hat{j} + 4\hat{k}).
Which of the following vectors is perpendicular to both (\vec{A} = \hat{i} + 2\hat{j} - 3\hat{k}) and (\vec{B} = 2\hat{i} - \hat{j} + 4\hat{k})?
Find the angle between the vectors (\vec{A} = \hat{i} + \hat{j}) and (\vec{B} = \hat{i} - \hat{j}).
Given a vector (\vec{A} = 3\hat{i} - 4\hat{j}), find the unit vector in the same direction as (\vec{A}).
Which of the following vectors is parallel to the vector (\vec{A} = 2\hat{i} - 3\hat{j})?
Find the area of the parallelogram formed by the vectors (\vec{A} = 2\hat{i} + 3\hat{j}) and (\vec{B} = 4\hat{i} - \hat{j}).
Which of the following vectors is a linear combination of the vectors (\vec{A} = \hat{i} + 2\hat{j}) and (\vec{B} = 2\hat{i} - \hat{j})?
Find the projection of the vector (\vec{A} = 2\hat{i} + 3\hat{j}) onto the vector (\vec{B} = 4\hat{i} - \hat{j}).
Which of the following vectors is orthogonal to both (\vec{A} = \hat{i} + 2\hat{j} - 3\hat{k}) and (\vec{B} = 2\hat{i} - \hat{j} + 4\hat{k})?