Question

If A=2i+j and B=j-k the magnitude of 2A+3B is

Answer 1

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Answer 2

Answer:

The magnitude of 2A+3B is 5√2 unit.

Explanation:

Given,A = 2i+j and B = j-k

Now,2A+3B = 2(2i+j)+3(j-k)

$= 4i + 2j + 3j - 3k \\ = 4i + 5j - 3k$

Here we want to find magnitude of 2A+3B.

Now question is how can I find magnitude?

If P= $xi + yj + zk$

then magnitude of P is |P| =

($\sqrt{ {x}^{2} + {y}^{2} + {z}^{2} }$) unit

For example If Q = i + 2j + 3k

Then |Q| =

$\sqrt{ {1}^{2} + {2}^{2} + {3}^{2} } \\ = \sqrt{1 + 4 + 9} \\ = \sqrt{14}$ unit

So,magnitude of 2A+3B is

$|2A+3B| = \sqrt{ {4}^{2} + {5}^{2} + {( - 3)}^{2} } \\ = \sqrt{16 + 25 + 9 \\ } \\ = \sqrt{25 + 25} \\ = \sqrt{50} \\ = 5 \sqrt{2}$

Therefore required magnitude of 2A+3B is 5√2 unit.

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