Chapter 3: Q9P (page 105)

Let $A = 2 i + 3 j$ and $B = 4 i - 4 j$ . Show graphically, and find algebraically, the vectors $- A, 3 B, A - B, B + 2 A, \frac{1}{2} (A + B)$ .

Short Answer

Expert verified

We use the rules of adding vectors graphically to solve this problem.

Step by step solution

Concept of vector

There are two ways to get the sum of two vectors. One is by the parallelogram law and the other is to find $A + B$ , place the tail of $B$ at the head of $A$ and draw the vector from the tail of $A$ to the head of $B$ .

Step 2: Calculating the vectors

Given: $A = 2 i + 3 j$ and $B = 4 i - 4 j$ .

$- A = - (2 i + 3 j) = - 2 i - 3 j$

which is shown in the following graph

$3 B = 3 (4 i - 4 j) = 12 i - 12 j$

As shown in the following graph

$∙ (A - B)$ vector:

$A - B = (2 i + 3 j) - (4 i - 4 j) = - 2 i + 7 j$

As shown in Graph

$∙ (B + 2 A)$ vector:

$B + 2 A = 4 i - 4 j + 2 (2 i + 3 j) = 4 i - 4 j + 4 i + 6 j = 8 i + 2 j$

Graph of the vector is as follows

$∙ (\frac{1}{2} (A + B))$ vector:

$\frac{1}{2} (A + B) = \frac{1}{2} (2 i + 3 j + 4 i - 4 j) = 3 i - \frac{1}{2} j$

The graph of the vector is shown below.

We use the rules of adding vectors graphically to solve this problem.

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Let $A = 2 i + 3 j$ and $B = 4 i - 4 j$ . Show graphically, and find algebraically, the vectors $- A, 3 B, A - B, B + 2 A, \frac{1}{2} (A + B)$ .

Short Answer

Step by step solution

Concept of vector

Step 2: Calculating the vectors

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Let A=2i+3jand B=4i-4j. Show graphically, and find algebraically, the vectors -A,3B,A-B,B+2A,12(A+B).

Short Answer

Step by step solution

Concept of vector

Step 2: Calculating the vectors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Astrophysics

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Study anywhere. Anytime. Across all devices.

Let $A = 2 i + 3 j$ and $B = 4 i - 4 j$ . Show graphically, and find algebraically, the vectors $- A, 3 B, A - B, B + 2 A, \frac{1}{2} (A + B)$ .