If a- - 5- - - - 7k-b- - - - - -k- find - - if a- - b- and - b- are orthogonal

( a + b )and( a b ) are orthogonal ( a + b ).( a b )=0 | a #160; | #160; ^ 2 | b #160; | #160; ^ 2 =0 | a # ...

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Applications of Dot Product

If a⃗ = 5î ...

Question

If $\to a = 5^i -^j + 7^k, \to b =^i -^j + λ^k$ find $λ,$ , if $\to a + \to b$ and $\to a - \to b$ are orthogonal

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Solution

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\to a = (5^i -^j + 3^k)

\to b = (^i + 3^j - 5^k)

(\to a + \to b)

(\to a - \to b)

\to a = 3^j - 2^j + 7^k, \to b = 5^i +^j - 2^k

\to c =^i +^j -^k

\to a \cdot (\to b \times \to c)

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

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

\to c =^i +^j -^k

\to a =^i -^j -^k

(\to a \times \to b) \times (\to c \times \to d)

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

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

λ + μ =

\to a =^i +^j, \to b =^i +^k

{{(\to a \times \to b) \times \to a} \times \to a} \times \to b =

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