Question

If v, = 3i+4j+k and v= i-j-k,
determine the magnitude of v1 +v2.​

Answer 1

Answer:

$|\vec V_1 + \vec V_2| = 5$

Explanation:

$\vec V_1 = 3 \hat i + 4\hat j + \hat k \\ \\ \vec V_2 = \hat i - \hat j - \hat k \\ \\ \vec V_1 + \vec V_2 = (3 + 1)\hat i + (4 - 1)\hat j + (1 - 1)\hat k \\ \\ \vec V_1 + \vec V_2 = 4\hat i + 3\hat j + 0\hat k \\ \\ \vec V_1 + \vec V_2 = 4\hat i + 3\hat j \\ \\ |\vec V_1 + \vec V_2 | = \sqrt{ {4}^{2} + {3}^{2} } \\ \\ = \sqrt{16 + 9} \\ \\ =\sqrt{25} \\ \\ |\vec V_1 + \vec V_2 | = 5$

Thus magnitude of v1+v2 = 5 units.

Hope it helps you.

Answer 2

Answer:

$|\vec V_1 + \vec V_2| = 5$

Explanation:

$\vec V_1 = 3 \hat i + 4\hat j + \hat k \\ \\ \vec V_2 = \hat i - \hat j - \hat k \\ \\ \vec V_1 + \vec V_2 = (3 + 1)\hat i + (4 - 1)\hat j + (1 - 1)\hat k \\ \\ \vec V_1 + \vec V_2 = 4\hat i + 3\hat j + 0\hat k \\ \\ \vec V_1 + \vec V_2 = 4\hat i + 3\hat j \\ \\ |\vec V_1 + \vec V_2 | = \sqrt{ {4}^{2} + {3}^{2} } \\ \\ = \sqrt{16 + 9} \\ \\ =\sqrt{25} \\ \\ |\vec V_1 + \vec V_2 | = 5$

Thus magnitude of v1+v2 = 5 units.