If vector a- - a1- - a2- - a3k- then- find unit vector-

a⃗ = a_1î + a_2ĵ + a_3k̂ | a⃗| = √(a_1^2 + a_2^2 + a_3^2) Unit vector = â = a_1î + a_2ĵ + a_3k̂√(a_1^2 + a_2^2 + a_3^2) ...

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Comparing Vectors

If vector a...

Question

If vector $\to a = a_{1}^i + a_{2}^j + a_{3}^k$ then, find unit vector.

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Solution

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\to a = a_{1}^i + a_{2}^j + a_{3}^k

| \to a \times \to i |^{2} + | \to a \times \to j |^{2} + | \to a \times \to k |^{2} = | 2 \to a |^{2}

¯ v = a_{1}^i + a_{2}^j + a_{3}^k

\to a = a_{1}^i + a_{2}^j - a_{3}^k

\to b = b_{1}^i + b_{2}^j - b_{3}^k

\to a \times \to b

\to a, \to b, \to c

a_{1}^i + a_{2}^j + a_{3}^k, b_{1}^i + b_{2}^j + b_{3}^k, c_{1}^i + c_{2}^j + c_{3}^k

= \to a \times (\to b + \to c) = \to a \times \to b + \to a \times \to c

a_{1}^i + a_{2}^j + a_{3}^k

b_{1}^i + b_{2}^j + b_{3}^k

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