Let = 2 î + 3 ĵ and = 2 î - 2 ĵ. Find the magnitude of the following.
(a) and (b) + (c) - - 2
typos?
Let = 2 î + 3 ĵ and = 2 î - 2 ĵ. Find the magnitude of the following.
(a) Eand F (b) E+F (c) -E – 2F
Do you read what you type? Do you perhaps mean
Let E = 2 î + 3 ĵ and F = 2 î - 2 ĵ. Find the magnitude of the following.
(a) E and F (b) E+F (c) -E – 2F
I will do two of them
magnitude of E = sqrt (4+9) = sqrt(13)
magnitude of E+F
= magnitude of 4 i + 1 j
= sqrt (16 + 1) = sqrt(17)
To find the magnitude of a vector, we use the formula:
Magnitude of a vector = √(x^2 + y^2)
(a) For vector a = 2î + 3ĵ, the magnitude is calculated as follows:
Magnitude of a = √(2^2 + 3^2)
= √(4 + 9)
= √13
Therefore, the magnitude of vector a is √13.
(b) For vector b = 2î - 2ĵ, the magnitude is calculated as follows:
Magnitude of b = √(2^2 + (-2)^2)
= √(4 + 4)
= √8
Since √8 can be simplified, we have:
Magnitude of b = √8 = √(4 * 2) = 2√2
Therefore, the magnitude of vector b is 2√2.
(c) For the expression -a - 2b, we need to calculate the vectors -a and -2b first.
The vector -a is obtained by multiplying each component of vector a by -1:
-a = -1(2î + 3ĵ) = -2î - 3ĵ
The vector -2b is obtained by multiplying each component of vector b by -2:
-2b = -2(2î - 2ĵ) = -4î + 4ĵ
Now, we can add -a and -2b:
-a - 2b = (-2î - 3ĵ) + (-4î + 4ĵ)
= -2î - 3ĵ - 4î + 4ĵ
= (-2î - 4î) + (-3ĵ + 4ĵ)
= -6î + ĵ
To find the magnitude of -a - 2b, we use the formula again:
Magnitude of (-a - 2b) = √((-6)^2 + 1^2)
= √(36 + 1)
= √37
Therefore, the magnitude of -a - 2b is √37.