Applications of Vector Algebra

The perpendicular distance from a point ( x₁, y₁ ,z₁ ) to the plane ax + by +cz = p is
The perpendicular distance from a point with position vector u̅ to the plane r̅.n̅ = p is
The distance between two parallel planes ax+by+cz+d₁ = 0 and ax+by+cz+d₂ = 0 is
The perpendicular distance from the origin to the plane ax+ by+ cz+ d = 0 is given by
Cartesian equation of the plane passing through three non-collinear points is
4. None
4. None
4. None
A particle acted upon by constant forces 2î+5ĵ+6k̂ and −î−2ĵ−k̂ is displaced from the point(4, −3, −2) to the point (6,1, −3) . Find the total work done by the forces.
1. 9
2. 8
3. 7
4. 6
A particle is acted upon by the forces 3î−2ĵ+2k̂ and 2î+ĵ−k̂ is displaced from the point (1,3,−1) to the point (4, 1,−λ) . If the work done by the forces is 16 units, find the value of λ .
1. −3
2. 4
3. −4
4. 3
Find the volume of the parallelepiped whose coterminus edges are given by the vectors
2î−3ĵ+4k̂ , î+2ĵ−k̂ and 3î−ĵ+2k̂
1. 7 cubic units
2. 6 cubic units
3. 9 cubic units
4. 12 cubic units
If 2î−ĵ+3k̂ , 3î+2ĵ+k̂ and î+mĵ+4k̂ are coplanar, find the value of m .
1. −2
2. −3
3. 3
4. 2
Find the acute angle between the lines r = (î+2ĵ+4k̂)+t(2î+2ĵ+k̂) and the straight line passing through the points (5,1, 4) and (9, 2,12)
1. sin⁻¹(2/3)
2. cos⁻¹(3/2)
3. sin⁻¹(3/2)
4. cos⁻¹(2/3)
1. π
2. π/2
3. π/4
4. None
1. ( 1, 1, 1)
2. ( −1, −1, −1)
3. ( −1, 1, −2)
4. ( −2, −1, 1)
1. √365/3
2. √365
3. √355/3
4. √345/3
Find the coordinates of the foot of the perpendicular drawn from the point ( −1, 2,3) to the straight line r = (î-4ĵ+3k̂)+t(2î+3ĵ+k̂)
1. ( -4 ,1 ,3 )
2. ( 3 ,1 ,-4 )
3. ( 3 ,-4 ,1 )
4. ( -4 ,3 ,3 )
A straight line which is perpendicular to a plane is called a ______ to the plane
1. normal
2. Tangent
3. Coplanar
4. None
For a given set of three vectors a̅ ,b̅ and c̅ , the scalar(a̅×b̅).c̅ is called
1. Scalar triple product
2. Vector triple product
3. Both A & B
4. None
For a given set of the scalar(a̅×b̅)×c̅ is called
1. Scalar triple product
2. Vector triple product
3. Both A & B
4. None
Two lines are said to be_____________if they lie in the same plane.
1. Coplanar
2. Skew lines
3. Normal
4. None

Applications of Vector Algebra

Quiz