Question
A non zero vector 
is parallel to the line of intersection of the plane determined by the vectors 
and the plane determined by the vectors 
then the angle between and 
is 
Hint:
We have to find the components of the vector parallel to the intersection of two planes. The planes are given using two vectors each. We have to find the angle between the parallel vector and another given vector. We will find the value of parallel vector by finding the line of intersection. Then, we will take the dot product.
The correct answer is:
The parallel vector is 
We have two vectors for each plane. Let the planes be Q and R.
The vectors for Q are as follows:
The vectors for R are as follows:
Let the another given vector be denoted by
We will find the normal to the planes by taking the cross product of the respective vectors.
Then by taking the cross product of normals, we will get the vector for line of intersection of two planes.
Let the normal to the first plane be denoted as 
The normal to the second plane is denoted by 
We will find the normals now
Now, to find the line of intersection we will take the cross product of normals.
Let the line be denoted as 
The angle between the line of intersection and the given vector will be same as the angle between the vector 
and the given vector.
To find the angle between them, we will use the dot product.
This is the required angle between the two vectors.
For such questions, we should know how to find the normal to the plane. We should know how to find the line of intersection of two planes. And, we should know how to take a cross product.
Related Questions to study
Let 
and 
. Then, the line of intersection of planes one determined by 
and other determined by 
is perpendicular to
For such questions, we should know how to find the line intersecting two planes. We should also know how to find the normal to the plane using two vectors.
Let and . Then, the line of intersection of planes one determined by and other determined by is perpendicular to
For such questions, we should know how to find the line intersecting two planes. We should also know how to find the normal to the plane using two vectors.
𝐀 𝐠𝐮𝐚𝐫𝐝 𝐨𝐟 𝟏𝟐 𝐦𝐞𝐧 𝐢𝐬 𝐟𝐨𝐫𝐦𝐞𝐝 𝐟𝐫𝐨𝐦 𝐧 𝐬𝐨𝐥𝐝𝐢𝐞𝐫𝐬.𝐈𝐟 𝐀 𝐚𝐧𝐝 𝐁 𝐚𝐫𝐞 𝐭𝐡𝐫𝐞𝐞 𝐭𝐢𝐦𝐞𝐬 𝐚𝐬 𝐨𝐟𝐭𝐞𝐧 𝐭𝐨𝐠𝐞𝐭𝐡𝐞𝐫 𝐨𝐧 𝐠𝐮𝐚𝐫𝐝 𝐚𝐬 𝐂, 𝐃, 𝐄 𝐭𝐡𝐞𝐧 𝐧 =
𝐀 𝐠𝐮𝐚𝐫𝐝 𝐨𝐟 𝟏𝟐 𝐦𝐞𝐧 𝐢𝐬 𝐟𝐨𝐫𝐦𝐞𝐝 𝐟𝐫𝐨𝐦 𝐧 𝐬𝐨𝐥𝐝𝐢𝐞𝐫𝐬.𝐈𝐟 𝐀 𝐚𝐧𝐝 𝐁 𝐚𝐫𝐞 𝐭𝐡𝐫𝐞𝐞 𝐭𝐢𝐦𝐞𝐬 𝐚𝐬 𝐨𝐟𝐭𝐞𝐧 𝐭𝐨𝐠𝐞𝐭𝐡𝐞𝐫 𝐨𝐧 𝐠𝐮𝐚𝐫𝐝 𝐚𝐬 𝐂, 𝐃, 𝐄 𝐭𝐡𝐞𝐧 𝐧 =
Number of ways of selecting 3 consecutive objects out of 15 objects (distinct) placed around a circle is
Number of ways of selecting 3 consecutive objects out of 15 objects (distinct) placed around a circle is
If 
, then 
If , then
The number of ways in which 6 gentlemen and 3 ladies be seated round a table so that every gentleman may have a lady by his side is
The number of ways in which 6 gentlemen and 3 ladies be seated round a table so that every gentleman may have a lady by his side is
If 
then the values of a and b are
If
then the values of a and b are
A circle having radius 7 touches both the axes and lies in 1st quadrant. If the circle is rolled along the positive x-axis and completes on rotation. Then equation of circle in final position is
A circle having radius 7 touches both the axes and lies in 1st quadrant. If the circle is rolled along the positive x-axis and completes on rotation. Then equation of circle in final position is
If 
For such questions, we should know different formulas.
If
For such questions, we should know different formulas.
Let α and β be the distinct roots of 
Let α and β be the distinct roots of
For such questions, we should know the different formulas of limits.
For such questions, we should know the different formulas of limits.
For such questions, we should know different formulae of limit.
For such questions, we should know different formulae of limit.
