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Scalar and Vector
1 / 10
1) The vector projection of a vector 3î + 4k̂ on y-axis is
Vector has no ĵ component only î and k̂, so projection on y-axis is 0.
2 / 10
3) If a particle moves from P(2,3,5) to Q(3,4,5), its displacement vector is
Q−P=(1,1,0)=î+ĵ.
3 / 10
8) Vector to be added to (î−3ĵ+2k̂) and (3î+6ĵ−7k̂) so resultant is unit vector along y-axis
Sum=(4,3,-5). Required=(0,1,0)-sum=(-4,-2,5).
4 / 10
6) Vector A makes equal angles with x,y,z axes. Each component equals
Direction cosines equal=1/√3.
5 / 10
10) Hall dimensions 10×12×14 m. Magnitude of displacement between opposite corners
Diagonal=√(10²+12²+14²)=√440≈21 m; provided options inconsistent.
6 / 10
2) Position of a particle in rectangular-coordinate system is (3, 2, 5). Then its position vector will be
Coordinates map directly to 3î + 2ĵ + 5k̂.
7 / 10
9) Minimum number of coplanar vectors of different magnitudes that can give zero resultant
Three unequal vectors can form a closed triangle.
8 / 10
7) If A⃗=2î+4ĵ−5k̂, direction cosines are
Magnitude=√45.
9 / 10
5) If A=3î+4ĵ and B=7î+24ĵ, vector having same magnitude as B and parallel to A is
|B|=25, unit A=(3/5,4/5), vector=25*(3/5,4/5)=(15,20).
10 / 10
4) A force of 5 N acts making 60° with the vertical. Its vertical component is
Vertical component=5 cos60°=2.5 N.
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