Looking for a Tutor Near You?

Post Learning Requirement » x
Ask a Question
x

Choose Country Code

x

Direction

x

Ask a Question

x

Hire a Tutor
Delhi

THE DOT OR SCALAR PRODUCT

Home > Study Notes > THE DOT OR SCALAR PRODUCT
Published in: Mathematics
1,924 Views

Here is an idea on finding the product of two vectors using the dot product method.

Unni K / Delhi

7 years of teaching experience

Qualification: B.Tech/B.E. (NERIST, Itanagar - 2011)

Teaches: Mathematics, B.Sc Tuition, Electronics, Physics, Electronics And Communication

Contact this Tutor
  1. THE DOT OR SCALAR PRODUCT. Two vectors can be multiplied together using the "dot/scalarproduct" to get a scalar number. Calculating The Dot Product gives a number as an answer (a "scalar", not a vector). The Dot Product is written using a central dot: This means the Dot Product of a and b We can calculate the Dot Product of two vectors this way: ä• B = lal x 1b x cos(0) Where : lal is the magnitude (length) of vector a lbl is the magnitude (length) of vector b 0 is the angle between a and b So we multiply the length of ä times the length of b, then multiply by the cosine of the angle between ä and b OR, we can calculate it this way: ä• = bx) + So we multiply the x's, multiply the y's, then add. Both methods work! ax : x-component of a ay : y-component of a bx .. x-component of b by . y-component of b by
  2. Example: Calculate the dot product of vectors a and b: -G = 66 From figure, ä = 6t + 8j; b = 5t + 12j 52 + 122 Now, ä• b = lal x 1b x cos(0) - 10 x 13 x cos(59.50) - 10 x 13 x 0.5075... - 65 98 . ... = 66 (rounded) -G = bx) + * = _ 30 + 96 = 13 a 12 59.5+ 13 8 10 x Both methods came up with the same result (after rounding) Also note that we used minus 6 for ax (it is heading in the negative x-direction) Q.l. Prove A • A Ans: Ä.É = 1B Icoso = IBI IAI Dot/Scalar product follows commutative law. (Commutative law means 2x3=3x2). Q.2. 5. Evaluate each of the following. Ans: (a) t - 3j + Q) = ltl ltl cos00 = t 1.1.1=1 cos90
  3. = î •2î -j • 31 + j • k = 20 • î) — 30 • j) + (j • k) = 2(0) 3(1) + (0) • (3î + k) = 2î • (3î + k) = 6(î • î) + 2(î • k) î) (j • k) = 6(1) + 2(0) - 3(0) - (0)

Need a Tutor or Coaching Class?

Post an enquiry and get instant responses from qualified and experienced tutors.

Post Requirement

Related Study Notes

Upload Study Notes

If you have your own Study Notes which you think can benefit others, please upload on LearnPick. For each approved Study Note you will get 50 Credit Points and 50 Activity Score which will increase your profile visibility.

Upload Now