Question

if p=2i+3j-4k and q= -4i+7j-5k find the Magnitude of p+q and p-q​

Answer 1

Explanation:

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Let O be the fixed point vector OP = position vector of P = 2 i + 3j + 4k = 2 3 4 vector OQ = position vector of Q = 3 i – 2 j – 3 k = 3 - 2 -3vector PQ = vector OQ – OP = 1 -5 -7 vector │PQ│= √ 1 + 25 + 49 = √75 Direction cosines of vector PQ are Cosα = 1/√ 75 Cosβ = -5/√ 75 & cosγ = - 7 /√ 75. Consider Cos2α + Cos2β + Cos2γ = 1/75 + 25 /75 + 49 /75 = 1