given vectors u=-9i+8j and v=7i+5j find 2u-6v in terms of unit vectors i and j
2 u = -18 i + 16 j
6 v = +42 i - 30 j
------------------------ subtract
- 60 i + 14 j
To find 2u - 6v in terms of unit vectors i and j, we need to multiply each vector by its respective scalar and then add them together.
Let's first calculate 2u:
2u = 2(-9i + 8j)
= -18i + 16j
Now, let's calculate 6v:
6v = 6(7i + 5j)
= 42i + 30j
Finally, let's find 2u - 6v:
2u - 6v = (-18i + 16j) - (42i + 30j)
To simplify further, we can combine like terms:
2u - 6v = -18i + 16j - 42i - 30j
Now, let's collect the terms with i and j separately:
2u - 6v = (-18i - 42i) + (16j - 30j)
= -60i - 14j
Therefore, 2u - 6v in terms of unit vectors i and j is -60i - 14j.
To find the expression 2u - 6v in terms of the unit vectors i and j, we need to multiply each vector component by the corresponding unit vector and then subtract the corresponding components.
First, let's write out the given vectors:
u = -9i + 8j
v = 7i + 5j
Now, let's find 2u:
2u = 2(-9i + 8j)
= -18i + 16j
Next, let's find 6v:
6v = 6(7i + 5j)
= 42i + 30j
Finally, let's subtract the resulting vectors:
2u - 6v = (-18i + 16j) - (42i + 30j)
= -18i + 16j - 42i - 30j
= (-18i - 42i) + (16j - 30j)
= -60i - 14j
Therefore, 2u - 6v in terms of unit vectors i and j is -60i - 14j.