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Given that `veca.vecb = 0` and `veca xx vecb = 0` What can you conclude about the vectors `veca and vecb`?
Concept: undefined >> undefined
Let the vectors `veca, vecb, vecc` given as `a_1hati + a_2hatj + a_3hatk, b_1hati + b_2hatj + b_3hatk, c_1hati + c_2hatj + c_3hatk` Then show that = `veca xx (vecb+ vecc) = veca xx vecb + veca xx vecc.`
Concept: undefined >> undefined
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If either `veca = vec0` or `vecb = vec0`, then `veca xxvecb = vec0`. Is the converse true? Justify your answer with an example.
Concept: undefined >> undefined
Find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).
Concept: undefined >> undefined
Find the area of the parallelogram whose adjacent sides are determined by the vector `veca = hati - hatj + 3hatk` and `vecb = 2hati - 7hatj + hatk`.
Concept: undefined >> undefined
Let the vectors `veca` and `vecb` be such that `|veca| = 3` and `|vecb| = sqrt2/3`, then `veca xx vecb` is a unit vector, if the angle between `veca` and `vecb` is ______.
Concept: undefined >> undefined
Area of a rectangle having vertices A, B, C, and D with position vectors `-hati + 1/2 hatj + 4hatk, hati + 1/2 hatj + 4hatk, and -hati - 1/2j + 4hatk,` respectively is ______.
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) cos^2 x dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) sqrt(sinx)/(sqrt(sinx) + sqrt(cos x)) dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) sin^(3/2)x/(sin^(3/2)x + cos^(3/2) x) dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (cos^5 xdx)/(sin^5 x + cos^5 x)`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_(-5)^5 | x + 2| dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_2^8 |x - 5| dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^1 x(1-x)^n dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/4) log (1+ tan x) dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^2 xsqrt(2 -x)dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (2log sin x - log sin 2x)dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_((-pi)/2)^(pi/2) sin^2 x dx`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_0^pi (x dx)/(1+ sin x)`
Concept: undefined >> undefined
By using the properties of the definite integral, evaluate the integral:
`int_(pi/2)^(pi/2) sin^7 x dx`
Concept: undefined >> undefined
