Find two vectors orthogonal to the given vector

Asked by maham237 @ 12/01/2021 in Mathematics viewed by 282 People

(1 point) Find two unit vectors orthogonal to a=⟨4,5,0⟩a=⟨4,5,0⟩ and b=⟨0,1,−3⟩b=⟨0,1,−3⟩ Enter your answer so that the first non-zero coordinate of the first vector is positive. First Vector: ⟨⟨ , , ⟩⟩ Second Vector: ⟨⟨ , , ⟩

Answered by maham237 @ 12/01/2021

Answer:

First vector

$V=+ \dfrac{-15i+12j+4k}{\sqrt{385}}$

Second vector

$V=- \dfrac{-15i+12j+4k}{\sqrt{385}}$

Step-by-step explanation:

Given that

Vector a , a= 4 i + 5 j + 0 k

Vector b , b= 0 i + 1 j - 3 k

The orthogonal vector V is given as

V = a x b

V is the cross product of the above two vector which is orthogonal to the vectors a and b.

$V=\begin{vmatrix}i & j & k\\ 4 & 5 & 0\\ 0& 1 &-3 \end{vmatrix}\\V=i(-15-0)-j(-12-0)+k(4-0)\\V=-15i+12j+4k$

The unit vectors

$V=\pm \dfrac{-15i+12j+4k}{\sqrt{15^2+12^2+4^2}}\\\\V=+\dfrac{-15i+12j+4k}{\sqrt{385}}\\V=-\dfrac{-15i+12j+4k}{\sqrt{385}}$

First vector

$V=+ \dfrac{-15i+12j+4k}{\sqrt{385}}$

Second vector

$V=- \dfrac{-15i+12j+4k}{\sqrt{385}}$

Resultant of two vectors a and b is given by

Asked by admin @ 04/08/2021 in Physics viewed by 293 persons

Resultant of two vectors A and B is given by |R|={|A|-|B|}, angles between A and B will be

Determine whether the given vectors are orthogonal parallel or neither

Asked by admin @ 30/09/2021 in Mathematics viewed by 317 persons

Determine whether the given vectors are orthogonal, parallel or neither. (a) u=[-3,9,6], v=[4,-12,-8,], (b) u=[1,-1,2] v=[2,-1,1] (c) u=[a,b,c] v=[-b,a,0]

Find the scalar and vector product of two vectors

Asked by admin @ 16/08/2021 in Physics viewed by 297 persons

find the scalar and vector product of two vectors A vector is equal to 3 i- 4j + 5 k and B vector -2 i + j - 3 k

Between two given rational numbers we can find

Asked by admin @ 26/08/2021 in Math viewed by 357 persons

Between two given rational number we can find

How to find the y intercept with two given points

Asked by admin @ 06/08/2021 in Math viewed by 343 persons

How to find y intercept when two points are given?

Find two sides of a right triangle given the hypotenuse

Asked by admin @ 10/11/2021 in Mathematics viewed by 331 persons

To solve for the hypotenuse of a right triangle, what information do you need? A. just the measure of one of the acute angles and the length of one side …

Find the angle between the given vectors to the nearest tenth of a degree. u = <8, 7>, v = <9, 7>

Asked by maham237 @ 23/12/2020 in Mathematics viewed by 320 persons

u = <8, 7>, v = <9, 7>

How to find other endpoint given one and a midpoint

Asked by admin @ 04/12/2021 in Mathematics viewed by 457 persons

What is the formula to find an endpoint when you are given one endpoint and the midpoint? example: Find the missing endpoint if S is the midpoint RT.R(-9, 4) and …

How to find area of a circle when given circumference

Asked by admin @ 29/11/2021 in Mathematics viewed by 310 persons

Explain each step in the process of finding the area of a circle given the circumference

How to find area of square when perimeter is given

Asked by admin @ 11/11/2021 in Mathematics viewed by 301 persons

A square has a perimeter of 25 inches. What is the area of the square?

How to find quadratic equation given vertex and a point

Asked by admin @ 10/11/2021 in Mathematics viewed by 327 persons

What is the quadratic function with the given vertex and through the given point? Write the equation of the parabola in vertex form and describe how the function was transformed …

How to find divergence and curl of a vector field

Asked by admin @ 10/11/2021 in Mathematics viewed by 290 persons

Find the curl and the divergence of the vector field f(x, y, z) = x2yz i + xy2z j + xyz2 k

Find the equation of a line given slope and point

Asked by admin @ 09/11/2021 in Mathematics viewed by 361 persons

Point Slope Formula POS Write the equation of a line given two points. (1.3) and (-3,-5) First, find the slope between the two lines and enter that answer below. Remember …

Find the equation of a line given point and slope

Asked by admin @ 09/11/2021 in Mathematics viewed by 365 persons

Point Slope Formula POS Write the equation of a line given two points. (1.3) and (-3,-5) First, find the slope between the two lines and enter that answer below. Remember …

Find equation of a line given slope and a point

Asked by admin @ 07/11/2021 in Mathematics viewed by 358 persons

Point Slope Formula POS Write the equation of a line given two points. (1.3) and (-3,-5) First, find the slope between the two lines and enter that answer below. Remember …