Chapter 9: Q. 18 (page 612)

Find b so that the vectors $v = i + j$ and $w = i + b j$ are orthogonal.

Short Answer

Expert verified

The value of $b$ is $- 1$ .

Step by step solution

Step 1. Concept Used

When two vectors uand vare orthogonal then their dot product is zero that is $u \cdot v = 0$ .

Step 2. Find the dot product

For the vectors $v = i + j$ and $w = i + b j$ the dot product is given as

$v \cdot w = (i + j) \cdot (i + b j) v \cdot w = 1 \cdot 1 + 1 \cdot b v \cdot w = 1 + b$

Step 3. Form the equation and solve for b

As the vectors $v$ and $w$ are orthogonal so their dot product is zero and so the equation is formed as

$\begin{array}{rcl} v \cdot w & = & 0 \\ 1 + b & = & 0 \end{array}$

On solving the equation we get

$\begin{array}{rcl} 1 + b - 1 & = & 0 - 1 \\ b & = & - 1 \end{array}$

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Find b so that the vectors $v = i + j$ and $w = i + b j$ are orthogonal.

Short Answer

Step by step solution

Step 1. Concept Used

Step 2. Find the dot product

Step 3. Form the equation and solve for b

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Find b so that the vectors v=i+j and w=i+bj are orthogonal.

Short Answer

Step by step solution

Step 1. Concept Used

Step 2. Find the dot product

Step 3. Form the equation and solve for b

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Statistics

Decision Maths

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Find b so that the vectors $v = i + j$ and $w = i + b j$ are orthogonal.