# math

posted by .

the position vectors of the point A,B & C respect to O are a=3i-2j+4k, b=i+3j-4k, c=-2i+5j-3k. Find
a)the angle between a+b and a-b
b)lamdar if vector a is perpendicular to b+lamdar k.

• math -

How do you define "lambdar" ?

As for part (a), compute these two vectors:
a + b = 4i +j +0k
a - b = 2i -5j +4k

Their magnitudes are:

|a+b| = sqrt(16 + 1) = sqrt17
|a-b| = sqrt(4 +25 + 16) = sqrt45

(a+b)*(a-b) = 8 -5 = 3
= (sqrt17) x (sqrt45) cos theta

cos theta = 3/sqrt765 = 0.108
theta = 83.8 degrees

In the above, * denotes a dot product and x denotes normal scalar multiplication

## Similar Questions

1. ### science (physics) Need to solve this today please

(a) Express the vectors A, B, and C in the figure below in terms of unit vectors. (b) Use unit vector notation to find the vectors R = A + B + C and S = C – A – B. (c) What are the magnitude and directions of vectors R and S?
2. ### Math: Vectors

Find any vector w that is perpendicular to both vector "u = 3j + 4k" and vector "v = 2i". Note: i, j and k are unit vectors How would you solve this problem?
3. ### Calculus

SORRY, i wrote this question wrong before ... u, v, w are UNIT VECTORS. the angle between u and v is 25 degrees and the angle between vector v and w is 35 degrees. find (v+w-3v). NOTE: vector u and w are on opposite sides of vector …
4. ### Math

The position vectors A and B with respect to the origin O,(-8,5) are (12,-5)and respectively. Point M is the midpoint of AB and N is the midpoint of OA. (a) Find: (i) The coordinates of N and M; (ii) The magnitude of NM, (b) Express …
5. ### math

The position vectors of points A and B with respect to the origin 0, are (-8,5) and (12,-5) respectively. Point M is the midpoint of B and N is the midpoint of OA. (a) Find: (i) The coordinates of N and M (ii) The magnitude of NM (b) …
6. ### math

The position vectors of points A and B with respect to the origin 0, are (-8,5) and (12,-5) respectively. Point M is the midpoint of B and N is the midpoint of OA. (a) Find: (i) The coordinates of N and M (ii) The magnitude of NM (b) …