if under root a cap minus b Cap is equal to under root 2 then calculate the value of modulus a cap + under root 3 b cap.
Answers
The value of modulus a^ +√3 b^ is 2.
Explanation:
=> It is given that, |a^ - b^| = √2
| a^ - b^ |² = |a^|² - 2<a^,b^> + |b^|²
| a^ - b^ |² = 1 - 2 <a^,b^> + 1 [<a,b> = 0 when unit vector are orthogonal]
| a^ - b^ |² = 1 + 1
| a^ - b^ |² = 2
| a^ - b^ | = √2
a^ - b^ = (√2)²
a^ - b^ = 2
=> The value of |a^ + √3b^| :
|a^ + √3b^|² = |a^|² + 2√3<a^,b^> + | √3b^|² [ <a^,b^ = 0 >]
|a^ + √3b^|² = (1)² + 2 √3 * 0 + (√3)²
|a^ + √3b^|² = 1 + 0 + 3
|a^ + √3b^|² = 4
|a^ + √3b^| = √4
|a^ + √3b^| = 2
Thus, the value of modulus a^ +√3 b^ is 2.
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Explanation:
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