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Let a⃗=2î+3...

Question

Let $\to a = 2^i + 3^j$ and $\to b =^i + 2^j$ . Then find $| \to a + \to b |$ .

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Solution

Given, $\to a = 2^i + 3^j$ and $\to b =^i + 2^j$ .
Now $\to a + \to b = 3^i + 5^j$ .
Then,
$|^a +^b | = \sqrt{3^{2} + 5^{2}} = \sqrt{34}$ .

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Similar questions

\to a = 2^i + 3^j + 2^k

\to b =^i + 2^j +^k

. Find the projection of

(i)

\to a

\to b

(i i)

\to b

\to a

Q. Obtain the angle between

\to A + \to B

\to A - \to B

\to A = 2^i + 3^j

\to B =^i - 2^j .

\to a = 2^i - 5^j + 8^k, \to b =^i - 3^j -^k, \to c = - 3^i - 2^j -^k

| \to a + \to b + \to c |

.

\to a = 2^i - 3^j +^k

\to b = 3^i + 2^j

\to a \times \to b

\to a = 3^i - 2^j +^k,

\to b = 2^i - 4^j - 3^k, \to c = -^i + 2^j + 2^k

\to a + \to b + \to c = 4^i - 4^j

\to a =^i -^j + 2^k, \to b = 2^i + 3^j +^k, \to c =^i -^k

, then magnitude of

\to a + 2 \to b - 3 \to c

\sqrt{78}

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