Vector Algebra

Classify the following measures as scalars and vectors.

Classify the following as scalar and vector quantities.

Answer the following as true or false.

Compute the magnitude of the following vectors:

Write two different vectors having same magnitude.

Write two different vectors having same direction.

Find the values of x and y so that the vectors 2î + 3ĵ and xî + yĵ are equal.

Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (-5, 7).

Find the sum of the vectors a⃗ = î - 2ĵ + k̂, b⃗ = -2î + 4ĵ + 5k̂ and c⃗ = î - 6ĵ - 7k̂.

Find the unit vector in the direction of the vector a⃗ = î + ĵ + 2k̂.

Find the unit vector in the direction of vector PQ, where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

For given vectors, a⃗ = 2î - ĵ + 2k̂ and b⃗ = -î + ĵ - k̂, find the unit vector in the direction of the vector a⃗ + b⃗.

Find a vector in the direction of vector 5î - ĵ + 2k̂ which has magnitude 8 units.

Show that the vectors 2î - 3ĵ + 4k̂ and -4î + 6ĵ - 8k̂ are collinear.

Find the direction cosines of the vector î + 2ĵ + 3k̂.

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

Show that the vector î + ĵ + k̂ is equally inclined to the axes OX, OY and OZ.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are î + 2ĵ - k̂ and -î + ĵ + k̂ respectively, in the ratio 2:1

Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, -2).

Show that the points A, B and C with position vectors,

respectively form the vertices of a right angled triangle.