Given vectors u=7i + 3j and v = -4i + 3j, find 5u-4v in terms of unit vectors.
I am just beginning the study of vectors and have this problem. Could someone help? Thanks.
handle them just like algebraic expressions
u=7i + 3j and v = -4i + 3j
then 5u - 4v
= 5(7i+3j) - 4(-4i+3j)
= 35i + 15j + 16i - 12j
= 51i + 3j
Dear Reiny,
Thank you for helping me. Could you check an answer for me?
Use a metric ruler and a protractor to find 2 a (vector) - 2 b (vector). Then find the magnitude and amplitude of the resultant.
Vector a is 4 cm and the angle is 60 degrees. Vector b is 1 centimeter long and the angle is 135 degrees.
My answer for magnitude was 4 cm with the angle being 31 degrees. Is this correct?
vector a = 4 cos 60 i + 4 sin 60 j
= 2 i + 0.866 j
vector b = -2.828 i + 2.828 j
"i" and "j" indicate the components along the x and y axes. It is a commonly used vector notation
a - b = -0.828 i + 3.694j
magnitude of a - b = 3.785
magnitude of 2 (a-b) = 7.571
Your angle is also wrong
Hi drwls--
I have just begun the study of vectors. I am given the answer in multiple choice--The answer you gave me is 7.571. The choices I have are 8cm;41 degrees; 9cm;38degrees;6cm,36degrees, and 4cm,31 degrees.
Your answer is closest to 8 cm. Is that the one I should select? Thanks.
Sure, I can help you with that! To find the expression 5u - 4v in terms of unit vectors, you can start by writing the given vectors in terms of their components.
Vector u, u = 7i + 3j
Vector v, v = -4i + 3j
Now, let's find the expression for 5u - 4v by multiplying the respective unit vectors with the scalar coefficients.
5u = 5(7i + 3j) = 35i + 15j
-4v = -4(-4i + 3j) = 16i - 12j
Now, subtract these two vectors to find 5u - 4v:
5u - 4v = (35i + 15j) - (16i - 12j)
To subtract the vectors, you can distribute the negative sign to each term inside the parentheses:
5u - 4v = 35i + 15j - 16i + 12j
Now, combine like terms:
5u - 4v = (35i - 16i) + (15j + 12j)
= 19i + 27j
Therefore, the expression 5u - 4v in terms of unit vectors is 19i + 27j.