First slide

Vectors

Question

A parallelogram is formed with a and b as the sides. Let d₁ and d₂ be the diagonals of the parallelogram. Then a² + b² = …..

Moderate

A

${d_{1}}^{2} + {d_{2}}^{2}$
B

$d_{1}^{2} - d_{2}^{2}$
C

$(d_{1}^{2} + d_{2}^{2}) / 2$
D

$(d_{1}^{2} - d_{2}^{2}) / 2$

Solution

d₁ = a+b and d₂= a -b
Now $d_{1}^{2} = a^{2} + b^{2} + 2 abcos θ$
and $d_{2}^{2} = a^{2} + b^{2} - 2 abcos θ$
$∴ a^{2} + b^{2} = (d_{1}^{2} + d_{2}^{2}) / 2$

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