PRACTICE PROBLEMS IN VECTOR WITH SOLUTION
About "Practice Problems in Vector With Solution"
Practice Problems in Vector With Solution :
Here we are going to see some practice problems in vector. You may also find solution for each problems.
Practice Problems in Vector - Questions
(1) Verify whether the following ratios are direction cosines of some vector or not.
(i) 1/5 , 3/5 , 4/5
(ii) 1/√2, 1/2 , 1/2
(iii) 4/3, 0, 3/4 Solution
(2) Find the direction cosines of a vector whose direction ratios are
(i) 1 , 2 , 3 (ii) 3 , - 1 , 3 (iii) 0 , 0 , 7 Solution
(3) Find the direction cosines and direction ratios of the following vectors.
(i) 3i vector - 4j vector + 8k vector
(ii) 3i vector + j vector + k vector
(iii) j vector
(iv) 5i vector - 3j vector - 48k vector
(v) 3i vector + 4j vector - 3k vector
(vi) i vector - k vector Solution
(4) A triangle is formed by joining the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). Find the direction cosines of the medians. Solution
(5) If 1/2, 1/√2, a are the direction cosines of some vector, then find a. Solution
(6) If (a , a + b , a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c. Solution
(7) Show that the vectors 2i − j + k, 3i − 4j − 4k, i − 3j − 5k form a right angled triangle. Solution
(8) Find the value of λ for which the vectors a = 3i + 2j + 9k and b = i + λj + 3k are parallel. Solution
(9) Show that the following vectors are coplanar
(i) i− 2 j + 3k, − 2i + 3j − 4k, − j + 2k
(ii) 5i + 6 j + 7k, 7i −8 j + 9k, 3i + 20j + 5k Solution
(10) Show that the points whose position vectors 4i + 5j + k, − j − k, 3i + 9j + 4k and −4i + 4j + 4k are coplanar. Solution
(11) If
find the magnitude and direction cosines of
(i) a vector + b vector + c vector
(ii) 3a vector - 2b vector + 5c vector Solution
(12) The position vectors of the vertices of a triangle are i+2j +3k; 3i − 4j + 5k and − 2i+ 3j − 7k . Find the perimeter of the triangle (Given in vectors) Solution
(13) Find the unit vector parallel to 3a − 2b + 4c if a = 3i − j − 4k, b = −2i + 4j − 3k, and c = i + 2 j − k Solution
(14) 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? Solution
(15) 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 Solution
(16) Find the value or values of m for which m (i + j + k) is a unit vector. Solution
(17) Show that the points A (1, 1, 1), B(1, 2, 3) and C(2, - 1, 1) are vertices of an isosceles triangle Solution
After having gone through the stuff given above, we hope that the students would have understood,"Practice Problems in Vector With Solution"
Apart from the stuff given in "Practice Problems in Vector With Solution", if you need any other stuff in math, please use our google custom search here.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
