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Test: Vector Algebra(25 Nov) - JEE MCQ


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15 Questions MCQ Test Daily Test for JEE Preparation - Test: Vector Algebra(25 Nov)

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Test: Vector Algebra(25 Nov) - Question 1

Direction angles are angles

Detailed Solution for Test: Vector Algebra(25 Nov) - Question 1

α,β,γ are the angles which the position vector  makes with the positive x-axis ,y-axis and z-axis respectively are called direction angles.

Test: Vector Algebra(25 Nov) - Question 2

 are any three vectors then the correct expression for distributivity of scalar product over addition is

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 are any three vectors then the correct expression for distributivity of scalar product over addition is :

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Test: Vector Algebra(25 Nov) - Question 3

Find the values of x and y so that the vectors 

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Test: Vector Algebra(25 Nov) - Question 4

Find the direction cosines of the vector 

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Test: Vector Algebra(25 Nov) - Question 5

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Test: Vector Algebra(25 Nov) - Question 6

Direction cosines

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Cosines of the angles α,β,γ are called direction cosines.

Test: Vector Algebra(25 Nov) - Question 7

Magnitude of the vector 

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We have : 

Test: Vector Algebra(25 Nov) - Question 8

Find the sum of the vectors    and  

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We have: 

Test: Vector Algebra(25 Nov) - Question 9

Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.

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Therefore, the D.C.’s of vector AB are given by: 

Test: Vector Algebra(25 Nov) - Question 10

If a unit vector makes angles π/3 with   and an acute angle θ with  then find θ

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Test: Vector Algebra(25 Nov) - Question 11

If l, m and n are direction cosines of the position vector OP the coordinates of P are

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If l , m and n are the direction cosines of vector  then , the coordinates of point P are given by : lr ,mr and nr respectively.

Test: Vector Algebra(25 Nov) - Question 12

Unit vectors along the axes OX, OY and OZ are denoted by 

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represents the unit vectors along the co ordinate axis i.e. OX ,OY and OZ respectively.

Test: Vector Algebra(25 Nov) - Question 13

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

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Test: Vector Algebra(25 Nov) - Question 14

Find the angle between two vectors  with magnitudes and 2, respectively, having 

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Test: Vector Algebra(25 Nov) - Question 15

If a unit vector  makes angles and an acute angle θ with , then the components of  are

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Let  It is given that left| , then , 





Putting these values in (1) , we get : 



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