-->

Vector Algebra

Question
CBSEENMA12036068

Let straight a with hat on top space and space straight b with hat on top be  two unit vectors. If the vectors straight c equals space straight a with hat on top space plus 2 straight b with hat on top and straight d space equals space 5 straight a with hat on top space minus 4 straight b with hat on top are perpendicular to each other, then the angle between straight a with hat on top space and space straight b with hat on top is 

  • π/6

  • π/2

  • π/3

  • π/4

Solution

C.

π/3

straight a with hat on top space and space straight b with hat on top space are space unit space vecotr comma space straight i. straight e comma space vertical line straight a with hat on top vertical line space equals space vertical line straight b with hat on top vertical line space equals 11
ii right parenthesis space straight C space equals straight a with hat on top space plus 2 straight b with hat on top space and space straight d space equals space 5 straight a with hat on top space minus 4 straight b with hat on top
(iii) c and d are perpendicular to each other, i.e., c.d =0
To find Angle between a and b
Now, c.d = 0
left parenthesis straight a with hat on top space plus 2 straight b with hat on top right parenthesis. left parenthesis 5 straight a with hat on top space minus 4 straight b with hat on top right parenthesis space equals space 0
rightwards double arrow space 5 straight a with hat on top. straight a with hat on top space minus space 4 space straight a with hat on top. straight b with hat on top space plus space 10 straight b with hat on top. straight a with hat on top space minus 8 space straight b with hat on top. straight b with hat on top space equals space 0
rightwards double arrow space 6 straight a with hat on top. straight b with hat on top space equals 3
rightwards double arrow space straight a with hat on top. straight b with hat on top space equals space 1 half
rightwards double arrow space vertical line stack straight a vertical line with hat on top vertical line straight b with hat on top vertical line space cos space straight theta space equals space cos space straight pi over 3
rightwards double arrow space Angle space between space straight a with hat on top space and space straight a with hat on top space is straight pi over 3

Some More Questions From Vector Algebra Chapter