MYTUTOR SUBJECT ANSWERS

652 views

What is the angle between the position vectors a and b, where a = (6i - j + 3k) and b = (-4i + 2j + 10k)?

cos(AOB) = a.b/(|a| x |b|)

a.b = (6i - j + 3k).(-4i + 2j + 10k)

      = (6 x -4) + (-1 x 2) + (3 x 10)

      = -24 + -2 + 30

      = 4

(|a|)^2 = 6^2 + (-1)^2 + 3^2

          = 36 + 1 + 9 = 46

          -> |a| = 46^(1/2)

(|b|)^2 = (-4)^2 + 2^2 + 10^2

          = 16 + 4 + 100 = 120

          -> |b| = 120^(1/2) = 2 x 30^(1/2)

cos(AOB) = a.b/(|a| x |b|)

               = 4/(46^(1/2) x 2 x 30^(1/2))

               = 4/(4 x 345^(1/2))

               = 1/(345^(1/2))

AOB = cos^-1 (1/(345^(1/)))

        = 86.9 degrees(3 significant figures)

David H. GCSE Biology tutor, A Level Biology tutor, GCSE Maths tutor,...

2 years ago

Answered by David, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

417 SUBJECT SPECIALISTS

Madeleine N. A Level Maths tutor, 11 Plus Maths tutor, 13 Plus  Maths...
£24 /hr

Madeleine N.

Degree: Natural Sciences (Masters) - Durham University

Subjects offered:Maths, Spanish+ 3 more

Maths
Spanish
Physics
Further Mathematics
-Personal Statements-

“Enthusiastic student, studying Maths and Physics at Durham university: keen to work hard with students to improve their results.”

£20 /hr

Rhianna C.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Chemistry+ 1 more

Maths
Chemistry
Biology

“I am currently studying Maths at University and absolutely love it! I can't wait to share my enthusiasm with you!”

£20 /hr

Scott E.

Degree: Computer Science (Bachelors) - Warwick University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Computing

“Maths and Computer Science lover. With a patient, thorough and friendly teaching style.”

About the author

David H.

Currently unavailable: for regular students

Degree: Medicine (Bachelors) - Exeter University

Subjects offered:Maths, Biology

Maths
Biology

“Me, myself and I I am a current medical student at Exeter University. I have loved science and maths from an early age, and have always looked for ways to increase my understanding of them – Horrible Science magazines were my favourit...”

You may also like...

Posts by David

Solve the simultaneous equations 3x + 4y = 17 and 4x + y = 14

What is meant by the semi-conservative replication of DNA?

What is the angle between the position vectors a and b, where a = (6i - j + 3k) and b = (-4i + 2j + 10k)?

Why is the heart known as a double pump?

Other A Level Maths questions

How can I derive an equation to find the sum of an arithmetic sequence?

Differentiate y = x^3 +x^2 - 4x +5 with respects to x.

If y = 5x^3 - 2x^2 + 2, what is dy/dx?

Draw y + 14 = x ( x - 4 ) and label all points of intersection with axes.

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok