Question

If a,b,c are three mutually perpendicular vectors of equal magnitude, find the angle between vectora and a+b+c

Answer 1

hope this hlp...........

Answer 2

angle between a and (a + b + c) is cos-¹(1/√3)

it is given that,

|a| = |b| = |c| [ magnitudes are equal. ] ......(1)

a, b, c are mutually perpendicular.

means, a.b = b.c = c.a = 0 ..... (2)

from equation (1) and (2),

|a + b + c| = √3|a| = √3|b| = √3|c| .......(3)

we have to find angle between a and (a + b + c)

a.(a + b + c) = |a|.|a + b + c|cosθ

⇒a.a + a.b + a.c = |a|√3|a|cosθ [ from equation (3)]

⇒|a|² + 0 + 0 = √3|a|²cosθ [ from equation (2) ]

⇒1/√3 = cosθ

⇒θ = cos-¹(1/√3)

also read similar questions: If a,b,c are mutually perpendicular unit vectors then show that det{a+b+c}=cube root of 3

https://brainly.in/question/1107891

Vectors A and B are mutually perpendicular . component of vector A+ vector B in direction of vector A - vector B will be...

https://brainly.in/question/10544414