Answer:
p = (2k + 1)i + j
q = 25i + (k + 4)j
p . q = 11
Find the dot product of p and q
(2k + 1)(25) + (k + 4) = 11
50k + 25 + k + 4 = 11
51k = -18
k = - 18/51 = –6/17.✅
b) p.q = |p||q|cos∅
p= (2k + 1)i + j = [2(-6/17) + 1)i + j ]= 5/17i + j
|p| = √ (5/17)² + 1²
|p| = √314/ 17 ( The square root doesn't cover the 17) = 1.0424
q = 25i + (k + 4)j = 25i + ( -6/17 + 4)j
q = 25i + 62/17 j
|q| = √ 25² + (62/17)²
= 25.2646
Now applying them to the formula above
We already have p.q = 11 from the question.
11 = (1.0424)(25.2646)Cos∅
11 = 26.3358Cos∅
Cos∅ = 11/26.3358
Cos∅ = 0.4177
∅ = 65.31°.
This should be it.
Hope it helps
I did it for you in the picture!
The problem cannot be fully solved because you did provide the line on which the line is parallel/ but i can give you the steps on how to solve it. first solve the slope of the parallel line by
m = ( y2 - y1 ) / ( x2 - x1 )
then the slope of that line is equal to slope of line passing pooint ( -1 , 1)
then solve the y intercept of the line using
y = mx + b
where b is the y intercept
then you will have the equation of the line
Answer:
Step-by-step explanation:
y - 1 = -25(x - 5)
y - 1 = -25x + 125
y = -25x + 126
Answer:
Maybe is 0,999999999999999....
Step-by-step explanation: