Question

if V has a magnitude of 14 units and the same direction qs a vector 3i+6j+2k find v​

Answer 1

Answer:

v = 6i + 12j + 4k

Explanation:

Find the magnitude of the direction vector.

√(3² + 6² + 2²) = 7

Normalize the direction vector.

3/7 i + 6/7 j + 2/7 k

Multiply by the magnitude of v.

v = 14 (3/7 i + 6/7 j + 2/7 k)

v = 6i + 12j + 4k

Answer 2

The vector  $\overrightarrow V$ = 6i + 12j + 4k

We have a vector $\overrightarrow V$ whose magnitude is 14 units and its direction is same as that of vector $\overrightarrow A$= 3i + 6j + 2k.

We have to find the vector $\overrightarrow V$.

If two vectors have same direction than what is the relation between their unit vectors?

If two vectors have the same direction, this means that they are parallel and hence have the same unit vectors.

According to the question, we have vector -

A  = 3i + 6j + 2k.

The magnitude of vector A will be -

|A| = $\sqrt{(3)^{2} +(6)^{2} +(2)^{2} }$ = $\sqrt{49}$ = 7

We know the following relation -

$\overrightarrow A = |A|a_{u}$  , where $a_{u}$ is the unit vector along the vector A.

$a_{u}$ = $\frac{\overrightarrow A}{|A|}$ = $\frac{1}{7} (3i + 6j + 2k)$

Now, we can calculate the vector V as -

$\overrightarrow V = |V|a_{u}$ = 14 x $\frac{1}{7} (3i + 6j + 2k)$ = 2 (3i + 6j + 2k) = 6i + 12j + 4k

Hence, the vector $\overrightarrow V$ = 6i + 12j + 4k.

To solve more questions on vectors, visit the link below -

https://brainly.com/question/11866267

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