Chapter 9: Q. 17 (page 612)

Find a so that the vectors $v = i - a j$ and $w = 2 i + 3 j$ are orthogonal.

Short Answer

Expert verified

The value of $a$ is $\frac{2}{3}$ .

Step by step solution

Step 1. Concept Used

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

Step 2. Find the dot product

For the vectors $v = i - a j$ and $w = 2 i + 3 j$ the dot product is given as

$v \cdot w = (i - a j) \cdot (2 i + 3 j) v \cdot w = 1 \cdot 2 + (- a) \cdot 3 v \cdot w = 2 - 3 a$

Step 3. Form the equation and solve for a

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

$\begin{array}{rcl} v \cdot w & = & 0 \\ 2 - 3 a & = & 0 \end{array}$

On solving the equation we get

$\begin{array}{rcl} 2 - 3 a - 2 & = & 0 - 2 \\ - 3 a & = & - 2 \\ \frac{- 3 a}{- 3} & = & \frac{- 2}{- 3} \\ a & = & \frac{2}{3} \end{array}$

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Find a so that the vectors $v = i - a j$ and $w = 2 i + 3 j$ 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 a

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Find a so that the vectors v=i-aj and w=2i+3j 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 a

One App. One Place for Learning.

Most popular questions from this chapter

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Find a so that the vectors $v = i - a j$ and $w = 2 i + 3 j$ are orthogonal.