Find sum of the vectors 3 - - 7 - - 4 k- and - - 5 - - 8 k- - - 5 - - 8 k- and hence find the unit vector along the sum of these vectors-

a⃗ =3i⃗ +7j⃗ 4k⃗ b⃗ =i⃗ 5j⃗ 8k⃗ Sum =A⃗ +B⃗ =3i⃗ +7j⃗ 4k⃗ +i⃗ 5j⃗ 8k⃗ C⃗ =4i⃗ +2j⃗ 12k⃗ unit vector in the direction of C⃗ = ...

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Standard XII

Mathematics

Definition of Vector

Find sum of t...

Question

Find sum of the vectors $3^i + 7^j - 4^k$ and $^i - 5^j - 8^k$ $^i - 5^j - 8^k$ and hence find the unit vector along the sum of these vectors.

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Solution

$\to a = 3 \to i + 7 \to j - 4 \to k \to b = \to i - 5 \to j - 8 \to k$
Sum $= \to A + \to B = 3 \to i + 7 \to j - 4 \to k + \to i - 5 \to j - 8 \to k$
$\to C = 4 \to i + 2 \to j - 12 \to k$
unit vector in the direction of $\to C$
$= \frac{4 \to i + 2 \to j - 12 \to k}{\sqrt{4^{2} + 2^{2} + 12^{2}}} = \frac{4 \to i + 2 \to j - 12 \to k}{\sqrt{164}} = \frac{4 \to i + 2 \to j - 12 \to k}{2 \sqrt{41}}$

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Find sum of the vectors 3^i+7^j−4^k and ^i−5^j−8^k ^i−5^j−8^k and hence find the unit vector along the sum of these vectors.

→a=3→i+7→j−4→k→b=→i−5→j−8→kSum =→A+→B=3→i+7→j−4→k+→i−5→j−8→k→C=4→i+2→j−12→kunit vector in the direction of →C=4→i+2→j−12→k√42+22+122=4→i+2→j−12→k√164=4→i+2→j−12→k2√41

Find sum of the vectors $3^i + 7^j - 4^k$ and $^i - 5^j - 8^k$ $^i - 5^j - 8^k$ and hence find the unit vector along the sum of these vectors.