Two vectors vecA and vecB have equal magnitudes. If magnitude of A + B is equal to two times the magnitude of A - B , then the angle between A and B will be:

Question

Two vectors vecA and vecB have equal magnitudes. If magnitude of A + B is equal to two times the magnitude of A - B , then the angle between A and B will be: (A)  sin -1((3/5)) (B)  sin -1((1/3)) (C)  cos -1((3/5)) (D)  cos -1((1/3))

Tardigrade Admin · Accepted Answer

(a2+b2+2 a b cos θ)=4(a2+b2-2 a b cos θ) put a=b we get 2 a2+2 a2 cos θ=8 a2-8 a2 cos θ cos θ=(3/5)

Q. Two vectors $A$ and $B$ have equal magnitudes. If magnitude of $A + B$ is equal to two times the magnitude of $A - B$ , then the angle between $A$ and $B$ will be:

$sin^{- 1} (\frac{3}{5})$

$sin^{- 1} (\frac{1}{3})$

$cos^{- 1} (\frac{3}{5})$

$cos^{- 1} (\frac{1}{3})$

$(a^{2} + b^{2} + 2 ab cos θ) = 4 (a^{2} + b^{2} - 2 ab cos θ)$
put $a = b$ we get
$2 a^{2} + 2 a^{2} cos θ = 8 a^{2} - 8 a^{2} cos θ$
$cos θ = \frac{3}{5}$

Q. Two vectors A and B have equal magnitudes. If magnitude of A+B is equal to two times the magnitude of A−B, then the angle between A and B will be:

sin−1(53​)

sin−1(31​)

cos−1(53​)

cos−1(31​)