How to Find Unit Vector Parallel to Given Vector :
Here we are going to see how to find unit vector parallel to given vector.
Question 1 :
Find the unit vector parallel to 3a − 2b + 4c if a = 3i − j − 4k, b = −2i + 4j − 3k, and c = i + 2 j − k
Let n vector = 3a − 2b + 4c
Unit normal vector = n vector/|n vector|
3a - 2b + 4c
= 3(3i − j − 4k) - 2(−2i + 4j − 3k) + 4(i + 2j − k)
n vector = 17i-3j-10k
|n vector| = √172 + (-3)2 + (-10)2
= √289 + 9 + 100)
Unit normal vector = (17i-3j-10k)/√398
Question 2 :
The position vectors a vector, b vector, c vector of three points satisfy the relation 2a vector - 7b vector + 5c vector. Are these points collinear?
Three distinct points A, B and C with position vectors a vector , b vector and c vector are collinear if and only if there exist real numbers x, y, z, none of them is zero, such that x + y + z = 0 and xa vector + yb vector + zc vector = 0.
In order to prove a, b and c are collinear, we have to find the sum of coefficient of a, b and c and prove it equal to 0.
x = 2, y = -7, z = 5
x + y + z = 2 + (-7) + 5 = 0
Hence the points a, b and c are collinear points.
Question 3 :
The position vectors of the points P, Q, R, S are i + j + k, 2i+ 5j, 3i + 2j − 3k, and i − 6j − k respectively. Prove that the line PQ and RS are parallel
OP vector = i + j + k
OQ vector = 2i+ 5j
OR vector = 3i + 2j − 3k
OS vector = i − 6j − k
PQ = OQ - OP
= (2i+ 5j) - (i + j + k)
PQ = (i + 4j - k) vector
RS = OS - OR
= (i − 6j − k) - (3i + 2j − 3k)
= (-2i - 8j + 2k) vector
RS = -2(i + 4j - k) vector
PQ = -2 RS
Hence PQ and RS are parallel.
After having gone through the stuff given above, we hope that the students would have understood,"How to Find Unit Vector Parallel to Given Vector"
Apart from the stuff given in "How to Find Unit Vector Parallel to Given Vector", if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Decimal place value worksheets
Area and perimeter
Different forms equations of straight lines
MATH FOR KIDS
HCF and LCM word problems
Word problems on quadratic equations
Word problems on comparing rates
Ratio and proportion word problems
Converting repeating decimals in to fractions