Question

If a b c are unit vectors such that a is perpendicular to the plane of b,c and the angle between b and c is pi/3 then what is |a+b+c|

Answer 1

Given Data

|a| = 1

|b| = 1

|c| = 1

Given a is perpendicular to plane of b, c.

So b × c = λ a

or, (a, b) = 90°

or, ( a, c) = 90°

Also Given,

( b, c) = pi/3 = 60°

Now Let's calculate dot products of the above vectors.

a. b = |a| |b| cos ( a, b)

= |a| |b| cos90°

= |a| |b| * 0

= 0

a. c = |a| |c| cos ( a, c)

= |a| |c| cos90°

= |a| |c| * 0

= 0

b. c = |c| |b| cos ( b, c)

= |c| |b| cos60°

= 1 * 1 * ½

= ½

Now,

⇒|a + b + c|² = |a|² + |b|² + |c|² + 2 ( a.b + a.c + b.c)

⇒ |a + b + c|² = 1² + 1² + 1² + 2 ( 0 + 0 + ½)

⇒|a + b + c|² = 1 + 1 +1 +1 = 4

⇒|a + b + c| = 2

Therefore, |a + b + c| = 2

Answer 2

Answer:

|a+b+c|=4

Step-by-step explanation:

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