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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Determine where a¯ and b¯ are orthogonal, parallel or neither. a¯=-35i^+12j^+13k^, b¯=5i^+4j^+3k^ - Mathematics and Statistics

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प्रश्न

Determine where `bb(bara)` and `bb(barb)` are orthogonal, parallel or neither.

`bara = -3/5hati + 1/2hatj + 1/3hatk ,  barb = 5hati + 4hatj + 3hatk`

बेरीज

उत्तर

`bara . barb = (-3/5hati + 1/2hatj + 1/3hatk).(5hati + 4hatj + 3hatk)`

= `(-3/5)(5) + (1/2)(4) + (1/3)(3)`

= −3 + 2 + 1

= 0

Since, `bara, barb` are non-zero vectors and `bara.barb` = 0.

`bara` is orthogonal to `barb`.

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पाठ 5: Vectors - Exercise 5.3 [पृष्ठ १६९]

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