To find the magnitude of the vector $ \mathbf{v} = 6\mathbf{i} + 2\mathbf{j} + 3\mathbf{k} $, we use the formula for the magnitude of a vector in three-dimensional space:

$$ \|\mathbf{v}\| = \sqrt{a^2 + b^2 + c^2} $$

where $ \mathbf{v} = a\mathbf{i} + b\mathbf{j} + c\mathbf{k} $.

In this case, $ a = 6 $, $ b = 2 $, and $ c = 3 $. Plugging these values into the formula, we get:

$$ \|\mathbf{v}\| = \sqrt{6^2 + 2^2 + 3^2} $$

Now, calculate each term inside the square root:

$$ 6^2 = 36 $$
$$ 2^2 = 4 $$
$$ 3^2 = 9 $$

Add these values together:

$$ 36 + 4 + 9 = 49 $$

Finally, take the square root of the sum:

$$ \|\mathbf{v}\| = \sqrt{49} = 7 $$

So, the magnitude of the vector $ 6\mathbf{i} + 2\mathbf{j} + 3\mathbf{k} $ is 7.

The correct answer is C7.

Question

To find the magnitude of the vector $ \mathbf{v} = 6\mathbf{i} + 2\mathbf{j} + 3\mathbf{k} $, we use the formula for the magnitude of a vector in three-dimensional space:

$$ \|\mathbf{v}\| = \sqrt{a^2 + b^2 + c^2} $$

where $ \mathbf{v} = a\mathbf{i} + b\mathbf{j} + c\mathbf{k} $.

In this case, $ a = 6 $, $ b = 2 $, and $ c = 3 $. Plugging these values into the formula, we get:

$$ \|\mathbf{v}\| = \sqrt{6^2 + 2^2 + 3^2} $$

Now, calculate each term inside the square root:

$$ 6^2 = 36 $$
$$ 2^2 = 4 $$
$$ 3^2 = 9 $$

Add these values together:

$$ 36 + 4 + 9 = 49 $$

Finally, take the square root of the sum:

$$ \|\mathbf{v}\| = \sqrt{49} = 7 $$

So, the magnitude of the vector $ 6\mathbf{i} + 2\mathbf{j} + 3\mathbf{k} $ is 7.

The correct answer is C7.

Knowee AI · Accepted Answer