Question

(Competition Section) 4.103 ngineering Entrace Exams 8. If A =B+and the values of A,B and are 13, 12 and 5 respectively, then the angle between A and C will be 5] 1 a) cos +(5/13) (c) 1/2 5 (b) cos=(13/12) (d) sin-l(5/12) 2 [IPUEE 09] л 9. The value of n so that the vectors ?​

Answer 1

Answer:

A2A

Method α :

Explanation:

A+B=C  

Using vector algebra to find the summation of two vectors,

(A^2 + B^2  + 2AB cosΦ)^ ( 1/2 ) =C  

{Here, A, B & C are the magnitudes of the respective vectors & Φ is the angle between A vector and B vector. }

Putting the values,

(12^2 + 5^2 + 2*12*5 cosΦ)^ ( 1/2 ) =13  

This implies,  cosΦ=0  

Therefore, the angle between A vector and B vector is 90°.

Method β :

It is very trivial to observe that the magnitudes of the vectors i.e. , 12,5 & 13 form a Pythagorean triplet. Hence, if we move the vectors in space and try to form a closed figure with them, then they will form a right angled Δ with hypotenuse 13 and sides 12 & 3 .

This implies that the angle between A vector and B vector is 90°.

Note that a vector doesn't change if you move it to any point without changing its orientation & magnitude.  

Hope it answers your question.

-KB