Find a unit vector that is orthogonal to both i + j and i + k.

Mathematics

1 answer:

kenny6666 [7]3 years ago

3 0

Answer: i - j - k

Step-by-step explanation:

Taking the cross product between two vectors will give you a third vector that is orthogonal(perpendicular) to both vectors.

<1,1,0> x <1,0,1>

$det(\left[\begin{array}{ccc}i&j&k\\1&1&0\\1&0&1\end{array}\right] )$

the determinate of the matrix: <1,-(1),-1>

or: i - j - k

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Given the list of terms 1/3, 1, 5/3, 7/3,.... Find the 15th and −16th term.

qwelly [4]

Answer:

15th term =29/3

16th term = 31/3

Step-by-step explanation:

Given an arithmetic sequence with the first term a1 and the common difference d , the nth (or general) term is given by an=a1+(n−1)d .

First we find the 15th term

n=15

a1=1/3

d=1 - 1/3 = 2/3

Solution

1/3+(15-1)2/3

1/3+28/3

(1+28)/3

29/3

Lets find the 16th term

1/3+(16-1)2/3

1/3+30/3

(1+30)/3

31/3

8 0

3 years ago

Keegan leans an 18-foot ladder against the top of a wall. The bottom of the ladder is 4.5 feet from the base of the wall. What i

zaharov [31]

Answer: C. 17.5 feet

Step-by-step explanation:

The attached photo shows the triangle ABC formed by the ladder and the wall. It is a right angle triangle because one of its angles is 90 degrees. The ladder is the hypotenuse of the triangle. To determine the height of the wall, we would find BC by applying Pythagoras theorem

Hypotenuse^2 = opposite ^2 + adjacent^2

18^2 + 4.5^2 + BC^2

BC^2 = 324 - 20.25 = 303.75

BC = √303.75 = 17.5 feet.