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In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.
4x + 8y + z – 8 = 0 and y + z – 4 = 0
Concept: undefined >> undefined
Find the angle between two vectors `veca` and `vecb` with magnitudes `sqrt3` and 2, respectively having `veca.vecb = sqrt6`.
Concept: undefined >> undefined
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Find the angle between the vectors `hati - 2hatj + 3hatk` and `3hati - 2hatj + hatk`.
Concept: undefined >> undefined
Find the projection of the vector `hati - hatj` on the vector `hati + hatj`.
Concept: undefined >> undefined
Find the projection of the vector `hati + 3hatj + 7hatk` on the vector `7hati - hatj + 8hatk`.
Concept: undefined >> undefined
Show that `|veca|vecb+|vecb|veca` is perpendicular to `|veca|vecb-|vecb|veca,` for any two nonzero vectors `veca and vecb`.
Concept: undefined >> undefined
If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC. [∠ABC is the angle between the vectors `bar(BA)` and `bar(BC)`].
Concept: undefined >> undefined
Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1) are collinear.
Concept: undefined >> undefined
Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z.
Concept: undefined >> undefined
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\[\int\left\{ x^2 + e^{\log x}+ \left( \frac{e}{2} \right)^x \right\} dx\]
Concept: undefined >> undefined
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Concept: undefined >> undefined
Concept: undefined >> undefined
