Q 50.

Question

Find a unit vector in the direction opposite to $<3, 4, 5>$ .

Step-by-Step Solution

Verified

Answer

The required vector is $\frac{1}{\sqrt{50}} <- 3, - 4, - 5>$ .

1Step 1. Given information.

The given vector is:

$v = <3, 4, 5>$

2Step 2. Find the norm of the vector.

$v = <3, 4, 5> ||v|| = \sqrt{3^{2} + 4^{2} + 5^{2}} = \sqrt{9 + 16 + 25} = \sqrt{50}$

Therefore, the norm of the given vector is $\sqrt{50}$ .

3Step 3. Find the vector.

We know that the vector in the direction of v is $\frac{1}{||v||} (- v)$ . Here a is the magnitude of the given vector and the negative sign shows the direction opposite to $v = <3, 4, 5>$ .

The required vector is:

$\frac{1}{||v||} v = \frac{1}{\sqrt{50}} (- <3, 4, 5>) = \frac{1}{\sqrt{50}} <- 3, - 4, - 5>$

Therefore, the unit vector in the direction opposite to $v = <3, 4, 5>$ is $\frac{1}{\sqrt{50}} <- 3, - 4, - 5>$ .

Q 49.

Q 51.

Other exercises in this chapter

Q 48.

Find a vector in the direction opposite to -4,5,-1 and with magnitude 3.

View solution

Q 49.

Find a vector in the direction opposite to 0,-3,4 and with magnitude 10.

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Q 51.

Find a vector of length 3 that points in the direction opposite to 1,-2,3.

View solution

Q. 52

Let P=(2,3,0,-1) and Q=(3,-2,1,6) be points in four-dimensional space.(a) Find PQ→.(b) Find PQO→.(c) Find the unit vector in the direction

View solution