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Vector Calculus
Prove that|(a ⃗+(b)) ⃗×(a ⃗-(b)) ⃗ | = 2ab. If a ⃗⊥ b ⃗.
Vector Calculus
Prove that (a ⃗+3b ⃗)×(a ⃗+b ⃗ )+(3a ⃗-5b ⃗)×(a ⃗-b ⃗) = 0.
Vector Calculus
Show that (a ⃗-d ⃗)×(b ⃗-c ⃗)+(b ⃗-d ⃗)×(c ⃗-a ⃗)+(c ⃗-d ⃗)×(a ⃗-b ⃗) is independent of d ⃗.
Vector Calculus
If a ⃗=(0,1 ,-1) and c ⃗= (1, 1, 1) are given vectors, then find a vector b ⃗ satisfying a ⃗×b ⃗+c ⃗ = 0 and a ⃗ .b ⃗ = 3.
Vector Calculus
Let a ⃗ = (3, -1, 0) and b ⃗=(1/2,3/2,1). Find the vector c ⃗satisfying a ⃗×c ⃗=4b ⃗ and a ⃗ .( c) ⃗=1.
Vector Calculus
Prove that (a ⃗/a^2 - b ⃗/b^2 )^2= ((a ⃗ - b ⃗)/ab )^2
Vector Calculus
The diagram of a parallelogram are given by a ⃗ = 3i ⃗-4j ⃗-k ⃗ and b ⃗=2i ⃗+3j ⃗-6k ⃗.
Vector Calculus
Find the vector of magnitude 3√2 which lies in ZX plane and is at right angle to the vector 2i ⃗+j ⃗+2k ⃗ .
Vector Calculus
If a ⃗=2i ⃗- j ⃗+ k ⃗ ,b ⃗= i ⃗- 3j ⃗-5k ⃗ find a vector c ⃗ such that a ⃗,b ⃗,c ⃗ form the sides of a right angled triangle taken in order .
Vector Calculus
magnitude of 3i-4j
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#340153 on Dec 2023
#340153 on Dec 2023