Question

Given P = 2i - 3] + 4k and Q
- 2k The magnitude of their resultant is​

Answer 1

Answer:

The angle between p and q is 90 degrees.

Explanation:

Vector, p=2i+3j-4kp=2i+3j−4k

Vector, q=5i+2j+4kq=5i+2j+4k

We need to find the angle between two vectors. It can be calculated using dot product formula.

Magnitude of |p|=\sqrt{2^2+3^2+(-4)^2} =5.385∣p∣=22+32+(−4)2=5.385

Magnitude of |q|=\sqrt{5^2+2^2+(4)^2} =6.70∣q∣=52+22+(4)2=6.70

Dot product formula,

p.q=|p||q|\ cos\thetap.q=∣p∣∣q∣ cosθ

cos\theta=\dfrac{p.q}{|p||q|}cosθ=∣p∣∣q∣p.q

cos\theta=\dfrac{(2i+3j-4k).(5i+2j+4k)}{5.385\times 6.70}cosθ=5.385×6.70(2i+3j−4k).(5i+2j+4k)

cos\theta=\dfrac{10+6-16}{36.079}cosθ=36.07910+6−16

cos\theta=0cosθ=0

\theta=90^{\circ}θ=90∘

So, the angle between p and q is 90 degrees. Hence, this is the required solution.

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