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For a particle undergoing circular motion with an angular velocity w in in a circle of radius r show that w×(w×r) = -w^2.r
) For a scalar field ( , , ) , n n n φ x y z = x + y + z show that (∇φ) r = nφ r r . , where n is a non-zero real constant.
5. Given that vectors a→=5i^−2j^+3k^ b→=3i^+j^−2k^ c→=i^−3j^+4k^ , calculate the scalar triple product a⃗ ⋅(b⃗ ×c⃗ ) 6. Given that vectors a→=5i^−2j^+3k^, b→=3i^+j^−2k^ and c→=i^−3j^+4k^ , calculate the vector triple product a⃗ ×(b⃗ ×c⃗ )
why there is no any particular rule to subtract vectors?
1 If ϕ=2xz4−x2y , find |▽ϕ| (√93) (√80) (√12) (√110) 2 If ϕ(x,y,z)=3x2y−y3z2 , find ▽ϕ at point (1,-2,-1) −12i−9j−16k i−3j−k 2i−5j−6k −3i−4j−2k 3 Find a unit normal to the surface x2y+2xz=4 at point (2,-2,3) 23i−23j−23k −15i+25j+25k −13i+23j+23k −17i+27j+27k 4 Let ϕ(x,y,z)=xy2z and A=xzi−xy2j+yz2k ,find ∂3∂x2∂z(ϕA) 2i+2j−5k 5i−k 4i−2j i+j 5 Given that ϕ=2x2y−xz3 find ▽2ϕ 2y−6xz 4y−6xz 2y−xz y+6xz 6 If A=xz3i−2x2yzj+2yz4 , find ▽×A at point (1,-1,1). 2j+3k 2i+j74k i+3j+5k 3j+4k 7 Given that A=A1i+A2j+A3k and r=xi+yj+zk , evaluate ▽⋅(A×r) if ▽×A=0 0 3 2 5 8 Let A=x2yi−2xzj+2yzk , find Curl curl A. 3j+4k 2x+2)k (2x+2)j 3j−4k 9 Given A=2x2i−3yzj+xz2k and ϕ=2z−x3y , find A⋅▽ϕ at point (1,-1,1). 5 3 4 1 10 Find the directional derivative of ϕ=x2yz+4xz2 at (1,-2,-1) in the direction 2i−j−2k 373 353 253 113
1 Find the angle between A=2x+2j−k and B=6i−3j+2k 600 450 690 790 2 Determine the value of a so that A=2i+aj+k and B=4i−2j−2k are perpendicular a=5 a=3 a=1 a=7 3 Determine a unit vector perpendicular to the plane of A=2i−6j−3k and B=4i+3j−k ±(37i−27j+67k) ±(35i+25j−65k) ±(14i−34j−12k) ±(−23i−13j+34k) 4 Find the work done in moving an object along a vector r=3i+2j−5k 3 5 7 9 5 Given that A=2i−j+3k and B=3i+2j−k , find A⋅B 3 6 1 9 6 If A=2i−3j−k and B=i+4j−2k , find (A+B+×(A−B) 3i+4j+25k 2i+6j+2k −20i−6j−22k −3i−5j−25k 7 If A=3i−j+2k , B=2i+j−k and C=i−2j+2k , find (A×B)×C 15i+15j−5k 5i+5j−5k −10i+10j−5k 15i+10j−5k 8 Determine a unit vector perpendicular to the plane of A=2i−6j−3k and B=4i+3j−k 35i−25j+65 17i−37j+47 37i−27j+67 27i−47j+57 9 Evaluate (2i−3j)⋅[(i+j−k)×(3i−k)] 4 5 6 8 10 If A=i−2j−3k , B=2i+j−k and C=i+3j−2k ,evaluate (A×B)⋅C -25 11 15 -20
Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <6, -2>, v = <8, 24> a. Neither b. Parallel c. Orthogonal
If A=x^z^3i−2^x^2yzj+2y^z^4 , find ▽×A at point (1,-1,1). 2j+3k \ 2i+j74k i+3j+5k 3j+4k
Let A=2x^2i−3yzj+xz^2k and ϕ=2z−x^3y , find A.▽ϕ at point (1,-1,1). 5 3 4 1
Let A=x^2yi−2xzj+2yzk , find Curl curl A. 3j+4k 2x+2)k (2x+2)j 3j−4k
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