Question

if A =2i cap +2j cap+3kcap and B=3icap-2j cap -4kcap​

Answer 1

Answer:

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Explanation:

Given that vectors,

a = 3i - 2j + k

b = i - 3j + 5k

c = 2i + j - 4k

We'll first calculate magnitudes of all vectors,

|a| = √(3^2 + 2^2 + 1^2)

|a| = √(9 + 4 + 1)

|a| = √14 units

|b| = √(1^2 + 3^2 +5^2)

|b| = √(1 + 9 + 25)

|b| = √35 units

|c| = √(2^2 + 1^2 + 4^2)

|c| = √(4 + 1 + 16)

|c| = √21 units

Angle between vectors a and c is calculated as -

cosθ = a.c / |a||c|

cosθ = (3i-2j+k).(2i+j-4k) / (√14.√21)

cosθ = (3×2-2×1-1×4) / √(14×21)

cosθ = 0

Taking cos inverse,

θ = arccos(0)

θ = 90°

Now let's take,

|a|^2 + |c|^2 = (√14)^2 + (√21)^2

|a|^2 + |c|^2 = 14 + 21

|a|^2 + |c|^2 = 35

|a|^2 + |c|^2 = (√35)^2

|a|^2 + |c|^2 = |b|^2