Question

if vector p + vector q = vector p - vector q and teta is angle between vector p and vector q then​

Answer 1

Answer:

Given that

p⃗ +q⃗ =p⃗ −q⃗

Taking self dot product on both the sides we get

(p⃗ +q⃗ )⋅(p⃗ +q⃗ )=(p⃗ −q⃗ )⋅(p⃗ −q⃗ )

p⃗ ⋅p⃗ +p⃗ ⋅q⃗ +p⃗ ⋅q⃗ +q⃗ ⋅q⃗ =p⃗ ⋅p⃗ −p⃗ ⋅q⃗ −p⃗ ⋅q⃗ +q⃗ ⋅q⃗

p2+2p⃗ ⋅q⃗ +q2=p2−2p⃗ ⋅q⃗ +q2

2p⃗ ⋅q⃗ =−2p⃗ ⋅q⃗

p⃗ ⋅q⃗ =0

pqcosθ=0

cosθ=0

θ=90∘

hence, the p⃗ & q⃗ are perpendicular to each other