Show That (a ⃗-b ⃗)×(a ⃗+b ⃗)=2a ⃗×b ⃗

Show That a ⃗ ×(b ⃗+c ⃗)+b ⃗ ×(c ⃗+a ⃗)+c ⃗ ×(a ⃗+b ⃗)=0

Find the scalar m such that the scalar product of i+j+k with unit vector parallel to the sum of 2i+4j-5k and mi+2j+3k is equal to unity.

show that a=3i-2j+k, b=i-3j+5k, c=2i+j-4k form a right angled triangle

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