Question

Find c if a = 0.3 i+0.4j+ck is a unit vector

Answer 1

Unit vector :

A vector whose magnitude is 1, is known as unit vector.

In vector notation, i, j, k are the unit vectors along the x, y, z axes respectively.

Given, a is a unit vector.

so,

Magnitude of a is 1

| a | = 1

Now,

1 = √ ( 0.3)² + ( 0.4)² + c²

1 = 0.09 + 0.16 + c²

1 - 0.25 = c²

c = √0.75

Used concept : Let a be a three dimensional vector, and a = xi^ + yj^ + zk^

then Magnitude of a is given by | a | = √(x²+y²+z²)

Hope helped!

Answer 2

Answer:

The value of c is 0.866.

Step-by-step explanation:

Given : If $a=0.3i+0.4j+ck$ is a unit vector.

To find : The value of c?

Solution :

We know that,

For a unit vector the magnitude is 1.

So, The magnitude of the unit vector $\vec{x}=ai+bj+ck$

$\sqrt{a^2+b^2+c^2}=1$

Substitute, a=0.3 , b=0.4, c=c

$\sqrt{0.3^2+0.4^2+c^2}=1$

$\sqrt{0.09+0.16+c^2}=1$

$\sqrt{0.25+c^2}=1$

Squaring both side,

$0.25+c^2=1$

$c^2=1-0.25$

$c^2=0.75$

$c=\sqrt{0.75}$

$c=0.866$

Therefore, The value of c is 0.866.