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Chapter 10 Vector Algebra Ex 10.3 Solutions

Question - 11 : - Show that  is perpendicular to , for any two nonzero vectors  .

Answer - 11 : -

Let us consider,

Question - 12 : - If  , then what can be concluded about the vector ?

Answer - 12 : -

We know

Question - 13 : - If   are unit vectors such that  , find the value of  .

Answer - 13 : -

Consider the given vectors,

Hence the value is -3/2.

Question - 14 : - If either vector , then  . But the converse need not be true. Justify your answer with an example.

Answer - 14 : -

Firstly,

Question - 15 : - If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC. [∠ABC is the angle between the vectors and ]

Answer - 15 : -

We know

Hence, the angle is cos-1 (10/ √102).

Question - 16 : - Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1) are collinear.

Answer - 16 : -

Let us consider
Given points are A (1, 2, 7), B (2, 6, 3), and C (3, 10, –1).
Now,

Therefore, the given points A, B, and C are collinear.

Question - 17 : - Show that the vectors form the vertices of a right angled triangle.

Answer - 17 : -

Firstly consider,

Question - 18 : -

Answer - 18 : -

Explanation:

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