Question

If a=2i-3j+k and b=i+4j-2k are two vectors then find (a+b)×(a-b).

Answer 1

Given A⃗ =2iˆ+3jˆ+4kˆ and B⃗ =3iˆ+4jˆ+5kˆ We know that A⃗ . B⃗ =∣∣A⃗ ∣∣ ∣∣B⃗ ∣∣ cosθor cosθ=A⃗ . B⃗ ∣∣A⃗ ∣∣ ∣∣B⃗ ∣∣=(2iˆ+3jˆ+4kˆ).(3iˆ+4jˆ+5kˆ)22+32+42√ 32+42+52√=3829×50√or cosθ=38558√=385×7.61=3839.05=0.9987or θ=cos−1(0.9987)=2.9°Therefore the angle between them is 2.9°.The magnitude of their resultant is; C=∣∣A⃗ ∣∣2+∣∣B⃗ ∣∣2+2∣∣A⃗ ∣∣ ∣∣B⃗ ∣∣cosθ−−−−−−−−−−−−−−−−−−−−√=29+50+29×50−−−−−−√×0.9987−−−−−−−−−−−−−−−−−−−−−−√or C=79+39.05×0.9987−−−−−−−−−−−−−−−−√=79+38−−−−−−√=117−−−√=10.8