Math Problem Statement

A ship sails due North 10√3 km, then 10 km due west, then its displacement is... (followed by various vector-related questions)

Solution

It seems you've uploaded an image from a textbook with vector-related questions. Let's break down the problem:

Question Breakdown:

  1. Q45 asks about a ship sailing and its displacement in polar form.
  2. Q46 involves vectors, determining when two vectors are perpendicular.
  3. Q47 explores a figure related to vector representation.
  4. Q48 asks for a calculation involving vectors A\mathbf{A} and B\mathbf{B}.

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Here are some related questions to consider:

  1. How do you convert vector displacement into polar coordinates?
  2. When are two vectors perpendicular? What condition do they satisfy?
  3. How do you represent a vector geometrically in polar form?
  4. How do you calculate vector addition and subtraction?
  5. What is the significance of the angle between two vectors?

Tip: When solving vector problems, always pay attention to the direction and magnitude, as they are key to understanding the vector's geometry and calculations.

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Math Problem Analysis

Mathematical Concepts

Vector addition
Polar coordinates
Perpendicular vectors
Vector magnitude and direction
Geometric representation of vectors

Formulas

Displacement formula in polar form
Dot product for perpendicular vectors
Vector addition formula

Theorems

Condition for perpendicular vectors (dot product equals zero)
Vector magnitude calculation

Suitable Grade Level

Grades 11-12