Pertanyaan

D ik e t ah u i v e k t or a = i + 6 j − k d an b = 7 i + 4 j + mk . J ika p anjan g p roye k s i v e k t or a k e v e k t or b s ama d e n g an 3 1 p anjan g v e k t or b , maka m = ⋯

$D ik e t ah u i v e k t or a = i + 6 j - k d an b = 7 i + 4 j + mk . J ika p anjan g p roye k s i v e k t or a k e v e k t or b s ama d e n g an \frac{1}{3} p anjan g v e k t or b, maka m = \dots$

4
4 atau 7
-4 atau 7
4 atau -7
-4 atau -7

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Pembahasan

$M i s a l k a n space p r o y e k s i space v e k t o r space a with rightwards arrow on top space k e space v e k t o r space b with rightwards arrow on top space a d a l a h space v e k t o r space c with rightwards arrow on top space d a n space p a n j a n g n y a space s a m a space d e n g a n space 1 third p a n j a n g space v e k t o r space space b with rightwards arrow on top comma space m a k a c with rightwards arrow on top equals 1 third space b with rightwards arrow on top K a r e n a space c with rightwards arrow on top equals open parentheses fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator vertical line b with rightwards arrow on top vertical line squared end fraction close parentheses b with rightwards arrow on top M a k a fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator vertical line b with rightwards arrow on top vertical line squared end fraction space equals space 1 third fraction numerator left parenthesis i plus 6 j minus k right parenthesis times left parenthesis 7 i plus 4 j plus m k right parenthesis over denominator vertical line 7 i plus 4 j plus m k vertical line squared end fraction equals 1 third fraction numerator 1 times 7 plus 6 times 4 plus left parenthesis negative 1 right parenthesis times m over denominator 7 squared plus 4 squared plus m squared end fraction equals 1 third fraction numerator 7 plus 24 minus m over denominator 49 plus 16 plus m squared end fraction space equals 1 third fraction numerator 31 minus m over denominator 65 plus m squared end fraction equals 1 third 3 left parenthesis 31 minus m right parenthesis equals 1 left parenthesis 65 plus m squared right parenthesis 93 minus 3 m equals 65 plus m squared m squared plus 3 m plus 65 minus 93 equals 0 m squared plus 3 m minus 28 equals 0 left parenthesis m plus 7 right parenthesis left parenthesis m minus 4 right parenthesis equals 0 S e h i n g g a m equals negative 7 a t a u m equals 4.$

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