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

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PRACTICE PROBLEMS IN VECTOR WITH SOLUTION

About "Practice Problems in Vector With Solution"

Practice Problems in Vector - Questions

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