Let the volume of a parallelopiped whose coterminous edges are given by and be 1 cu. unit. If be the angle between the edges and then can be :
Option: 1
Option: 2
Option: 3
Option: 4
Dot (Scalar) Product in Terms of Components -
Angle between two vectors
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Geometrical Interpretation of Scalar Triple Product -
Let vectors and represented the sides of a parallelepiped OA, OB and OC respectively. Then, is a vector perpendicular to the plane of and . Let ? be the angle between vectors and and α be the angle between and .
If is a unit vector along , then α is the angle between and .
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Correct Option (3)
View Full Answer(1)Let and be two vectors. If is a vector such that and then is equal to :
Option: 1
Option: 2
Option: 3
Option: 4
Vector Triple Product -
For three vectors and vector triple product is defined as .
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Correct Option (3)
View Full Answer(1)Let and be three unit vectors such that .If and then the ordered pair, is equal to :
Option: 1
Option:2
Option: 3
Option: 4
Addition and subtraction of Vectors -
Properties of vector addition
The sum of two vectors is always a vector.
Properties of vector Subtraction
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Correct Option (3)
View Full Answer(1)Let be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle , with the vector . Then is equal to ________.
Given,
and these are mutually perpendicular,
So,
Angle of with
Now,
Using this in (i)
Hence, the correct answer is 4
View Full Answer(1)Study 40% syllabus and score up to 100% marks in JEE
Let . Let a vector be in the plane containing . If is perpendicular to the vector and its projection on is 19 units, then is equal to___________
(a vector in the plane of & and perpendicular to )
Give expression is
OR
option (4)
...............(1)
..........(2)
From (1) and (2)
So
Also
So
Angle
View Full Answer(1)
Let be three vectors such that, is perpendicular to . Then the greatest amongst the values of is__________
If the projection of the vector on the sum of the two vectors and is 1, then is equal to ________.
Sum of vectors ( ) is
Projection of on is
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Let the volume of a parallelopiped whose coterminous edges are given by
Let and be three unit vectors such that
Let be three vectors mutually perpendicular to each other and have same magnitude. If a vector
The angle between the straight lines, whose direction cosines are given by the equations
If the projection of the vector on the sum of the two vectors