Vector Algebra Class 12 Notes - Chapter 10

Position of a Vector

If we are provided with a point Q(x,y,z) and

CBSE Class 12 Maths Notes Chapter 10 Vector Algebra – Related Links

• Vector Algebra
• Vectors

The relation between magnitude, direction ratios, and direction cosines of a vector

If a vector has been given with dimensions such as magnitude(p), direction ratios (x,y,z) and direction cosines (l,m,n) then the relation between them is:

l=x/p, m=y/p,n=z/p

The order taken for the vector sum of the three sides of the triangle is

And the vector sum of coinitial vectors is the diagonal of the parallelogram, which has the vectors as its adjacent sides.

When multiplying a vector by a scalar λ, the magnitude of the vector changes by the multiple |λ|, and the direction remains the same (or makes it opposite) according to the value of λ being positive (or negative).

Position Vector of a Point R on a Line Segment

A line segment joining two points, such as P having a position vector of

• The internal ratio is given by
  \(\begin{array}{l}n\underset{a}{\rightarrow}+m\underset{b}{\rightarrow}/m+n\end{array} \)
• The external ratio is given by

The scalar product of two position vectors

We can find the value of

Important Questions

1. Find the ratio in which B divides AC and also show that points A(2, – 3, – 9), B(6, 0, –1), and C(10, 4, 6) are not collinear.
2. Determine the girl’s displacement from her initial point of departure if she walks 5 km towards the West, then walks 4 km in a direction 40° East of the North and stops.
3. Draw a unit vector in the XY-plane, making an angle of 30° with the positive direction of the x-axis.
4. Find the area of the triangle with vertices P(2, 3, 4), Q(3, 4, 6) and R(2, 6, 7).
5. Show that the points P(1, 2, 7), Q(2, 6, 3) and R(3, 10, –1) are collinear

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