Question

3.If P = 2i +4j+14k and Q=4i +4j+10k find the magnitude of P+Q.
​

Answer 1

Given:

$\rm \overrightarrow{P} = 2\hat{i } + 4\hat{j} + 14\hat{k} \\ \rm \overrightarrow{Q} = 4\hat{i} + 4\hat{j} + 10\hat{k}$

To Find:

$\rm | \overrightarrow{P} + \overrightarrow{Q} |$

Answer:

$\rm \implies \overrightarrow{P} + \overrightarrow{Q} = (2\hat{i } + 4\hat{j} + 14\hat{k}) + (4\hat{i} + 4\hat{j} + 10\hat{k}) \\ \\ \rm \implies \overrightarrow{P} + \overrightarrow{Q} = 2\hat{i } + 4\hat{i}+ 4\hat{j} + 4\hat{j} + 14\hat{k} + 10\hat{k} \\ \\ \rm \implies \overrightarrow{P} + \overrightarrow{Q} = 6\hat{i } + 8\hat{j} + 24\hat{k} \\ \\ \rm \implies | \overrightarrow{P} + \overrightarrow{Q} | = \sqrt{ {6}^{2} + {8}^{2} + {24}^{2} } \\ \\ \rm \implies | \overrightarrow{P} + \overrightarrow{Q} | = \sqrt{36 + 64 + 576} \\ \\ \rm \implies | \overrightarrow{P} + \overrightarrow{Q} | = \sqrt{676} \\ \\ \rm \implies | \overrightarrow{P} + \overrightarrow{Q} | = 26$

$\therefore$ $\boxed{\mathfrak{|\overrightarrow{P} + \overrightarrow{Q} | = 26}}$

Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

ɪꜰ ᴘ = 2ɪ +4ᴊ +14ᴋ ᴀɴᴅ Q = 4ɪ +4ᴊ+10ᴋ ꜰɪɴᴅ ᴛʜᴇ ᴍᴀɢɴɪᴛᴜᴅᴇ ᴏꜰ ᴘ + Q.

♣ ɢɪᴠᴇɴ :

$\bf{\overrightarrow{P}=2i +4j+14k}$

$\bf{\overrightarrow{Q}=4i +4j+10k}$

♣ ᴛᴏ ꜰɪɴᴅ:

$\lvert {\overrightarrow{P}+{\overrightarrow{Q} \rvert$

♣ ᴀɴꜱᴡᴇʀ:

$\bigstar\:\bf{\overrightarrow{P}}+\bf{\overrightarrow{Q}} =\bf{(2i +4j+14k)+(4i +4j+10k)}$

$\Rightarrow\:\bf{\overrightarrow{P}}+\bf{\overrightarrow{Q}} = \bf{2i +4j+14k+4i +4j+10k}$

$\Rightarrow\:\bf{\overrightarrow{P}}+\bf{\overrightarrow{Q}} = \bf{6i + 8j + 24k}$

                                       

$\bigstar\: \bf{Magnitude\:\: of \:\:\overrightarrow{a}=\lvert{\overrightarrow{a}\rvert$

$\bf{\lvert{\overrightarrow{a}\rvert=\sqrt{x^2+y^2+z^2}}$

                                       

$\bigstar\:\bf{\lvert {\overrightarrow{P}+{\overrightarrow{Q} \rvert = \sqrt{6^2 + 8^2 +24^2}}$

$\bf{\lvert {\overrightarrow{P}+{\overrightarrow{Q} \rvert = \sqrt{36 + 64 + 576}}$

$\bf{\lvert {\overrightarrow{P}+{\overrightarrow{Q} \rvert = \sqrt{676}}$

$\bf{\lvert {\overrightarrow{P}+{\overrightarrow{Q} \rvert = 24}$