Question

If d1 = 3i-2j + 4k and d2 = -5i + 2j-k, determine (d1 + d2). (d1 × 4d2).

Answer 1

Given info : two vectors d₁ = 3i - 2j + 4k and d₂ = -5i + 2j - k

To find : the value of (d₁ + d₂).(d₁ × 4d₂)

solution : Here, (d₁ + d₂) = (3i - 2j + 4k) + (-5i + 2j - k)

= -2i + 0j + 3k

4d₂ = 4(-5i + 2j - k)

= -20i + 8j - 4k

Now, d₁ × 4d₂ = (3i - 2j + 4k) × (-20i + 8j - 4k)

= (-2 × -4 - 4 × 8)i - (3 × -4 - 4 × -20)j + (3 × 8 - (-2) × -20)k

= - 24i - 68j - 16k

Now, (d₁ + d₂).(d₁ × 4d₂)

= (-2i + 0j + 3k).(- 24i - 68j - 16k)

= -2 × -24 + 0 × -68 + 3 × -16

= 48 + 0 - 48

= 0

Therefore the value of (d₁ + d₂).(d₁ × 4d₂) is 0