Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
The values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively. This can be obtained by using vector addition, vector subtraction and formula to find magnitude of a vector.
Find the values of a + b, 6a + 9b, |a|, and |a − b|:
Given that,
a = <−9, 12> , b = <6, 4>
These vectors can be rewritten as,
a = <−9, 12> = −9i + 12j
b = <6, 4> = 6i + 4j
- To find a + b,we add both vectors a and b together,
a + b = −9i + 12j + 6i + 4j
a + b = −9i + 6i + 12j + 4j
a + b = (−9 + 6)i + (12 + 4)j
a + b = −3i + 16j
- To find 6a + 9b, we first find 6a and 9b then add them both together,
6a = 6 (−9i + 12j )
6a = −54i + 72j
9b = 9(6i + 4j)
9b = 54i + 36j
Now add 6a and 9b together,
6a + 9b = −54i + 72j + 54i + 36j
6a + 9b = −54i + 54i + 72j + 36j
6a + 9b = 0i + 108j
- To find |a|, use the formula to find the magnitude of a vector,
If a = a₁i + a₂j, |a| = √a₁² + a₂²
Here, a = −9i + 12j
|a| = √(−9)² + (12)²
|a| = √81 + 144 = √225
|a| = 15
- To find |a − b|, first subtract b from a and find the magnitude of the resultant,
a - b = −9i + 12j - (6i + 4j)
a - b = −9i - 6i + 12j - 4j
a - b = −15i + 8j
Now use the formula to find the magnitude of a vector,
|a − b| = √(-15)² + (8)²
|a − b| = √225 + 64 = √289
|a − b| = 17
Hence the values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively.
Learn more about magnitude of a vector here:
brainly.com/question/27870005
#SPJ1
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
