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2 years ago

Easy vector problem! show work/explain please :)

Mathematics

1 answer:

krek1111 [17]2 years ago

8 0

Answer:

Step-by-step explanation:

a = 2i + 3j + zk

b = xi + 1j + 4k

Given a X b = 6i -14j +5k

a X b = | i j k|

|2 3 z|

|x 1 4|

a X b = i(12-z) - j(8 - xz) + k(2-3x) = 6i -14j +5k

equate the coefficients of i , j and k

12- z = 6; implies z = 6

8 - xz = -14 implies 8 - 6x = -14

2-3x = 5 implies 2 - 3x = 5 implies x = -1

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) The points (1, 0, 3), (1, 1, 1), and (−2, −1, 2) lie on a unique plane a1x1 + a2x2 + a3x3 = b. Using your previous answers, fi

Rudik [331]

Answer:

x1-2x2-x3= -2

Step-by-step explanation:

Substitute the three points to get three equations:

a1+0a2+ 3a3=d --------------eq i

a1+a2+a3=d----------------eq ii

-2a1-a2+2a3=d---------------eq iii

subtract eq i from eq ii

a2-2a3=0 ----------- eq iv

now add eq iv to eq iii

-2a1=d ------- eq v

put eq v in eq i

a1 + 3a3=-2a1

a3= -a1 ----------- eq vi

put eq vi in eq iv

a2-2(-a1)=0

a2= -2a1 ------ eq vii

put eq v, eq vi and eq vii in the equation of plane

a1x1+ a2x2+a3x3=d

a1x1 -2a1x2-a1x3=-2a1

x1-2x2-x3= -2

6 0

3 years ago

Read 2 more answers

What is the value of x in this equation?

elena-14-01-66 [18.8K]

Answer:

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Mildred’s salary has increased from £24,600 to £25,338. By what percentage has her salary increase?

Illusion [34]

Answer:

<h3>The answer is 3%</h3>

Step-by-step explanation:

To find the percentage increase we use the formula

$Percentage \: change = \frac{ change}{original \: quantity} \times 100$

To find the change subtract the smaller quantity from the bigger one

From the question

original price = $24,600

Current price = $ 25,338

Change = $25,338 - $ 24,600

Change = $ 738

So the percentage increase is

$\frac{738}{24600} \times 100$

$= \frac{3}{100} \times 100$

We have the final answer as

<h3>Percentage increase = 3%</h3>

Hope this helps you

3 0

3 years ago

The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?(A)

ZanzabumX [31]

Answer:

A:102

Step-by-step explanation:

We are given that the points A(0,0),B(0,4a-5) and C(2a-+1,2a+6) form a triangle.

If angle ABC= $90^{\circ}$

We have to find the area of triangle ABC

If angle ABC= 90 degree

From given below figure

$4a-5=2a+6$

$4a-2a=6+5$

$2a=11$

$a=\frac{11}{2}=5.5$

Substitute the values then we get

B(0,17) and C (12,17)

Distance formula

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

AB= $\sqrt{(0-0)^2+(17-0)^2}=17 units$

BC= $\sqrt{(12-0)^2+(17-17)^2}$

BC= $\sqrt{144+0}=\sqrt{144}=12$ units

Area of triangle = $\frac{1}{2}\times b\times h$

Substitute the values

Then we get

Area of triangle ABC= $\frac{1}{2}\times 17\times 12$

Area of triangle ABC=102 square units

Answer: A: 102

8 0

3 years ago

(6x 7)(6x-7) determine each product

Drupady [299]

(6x7) = 47
(6x-7) = -42 -- This is because you are multiplying two differently signed numbers, the product will be negative.

5 0

3 years ago