Geometric Vectors: 동영상 및 연습문제

Draw the resultant vector for the pair of vectors with angle α between them using the given information.

|a| = 7, |b| = 15, α = 54°

Given the following vector, v, obtain the unit vector (u) that aligns with the direction of  v.

v = 16 i - 12 j

Considering the vector a = 11i - 4j, determine the following vector:

30a

Find 7a - (3b - 2c) using the following vectors:

a = -5i + 6j, b = 2i + 7j, c = 10i + 9j

For the given vector, calculate its magnitude and direction angle. Express your answer to the nearest tenth, if required.

$〈11, 14〉$

Express the following vector into terms of $\(\textbf{i}\)$ and $\(\textbf{j}\)$ .

$〈9, -11〉$

For the following vectors, Find the value of the following expression $(8\(\text{\textbf{u}\)}) • \(\text{\textbf{v}\)}$ .

$\(\text{\textbf{u}\)}=〈-10,6〉$ and $\(\text{\textbf{v}\)}=〈12,19〉$

Two Siberian Huskies are pulling a sled on a snowy terrain. The forces exerted by these dogs on the sled are 16 lb, and 5 lb, and the angle between these forces is 18.3°. Determine the magnitude of the equilibrant and the angle it makes with the 16 lb force.

A motorboat departs 10.4 miles out of port with a bearing of 313°. After a few hours, the motor makes a turn and starts moving to the west for 6.9 mi. Find the bearing of the ship and its distance from the port.

Which of the following best describes a vector?

In vector representation, what do the initial and terminal points of an arrow signify?

If a vector is represented by an arrow that is 5 units long, what is the magnitude of the vector?

A vector makes a 45-degree angle with the east direction. What is the direction of the vector?

What happens to a vector when it is negated?

Which of the following is true about the zero vector?

Using the tip-to-tail method, if vector A is 3 units east and vector B is 4 units north, what is the direction of the resultant vector?

Which of the following statements is true regarding vector operations?

If vector A is 2 units east and is multiplied by a scalar of 3, what is the new magnitude and direction of the vector?

A car travels 60 km/h north. Is this an example of a vector or a scalar?

Given a vector represented by an arrow from point A (2, 3) to point B (5, 7), what are the initial and terminal points?