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The vector equation of the line through the points (3, 4, –7) and (1, –1, 6) is ______.
Concept: undefined >> undefined
The cartesian equation of the plane `vecr * (hati + hatj - hatk)` is ______.
Concept: undefined >> undefined
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The unit vector normal to the plane x + 2y +3z – 6 = 0 is `1/sqrt(14)hati + 2/sqrt(14)hatj + 3/sqrt(14)hatk`.
Concept: undefined >> undefined
The intercepts made by the plane 2x – 3y + 5z +4 = 0 on the co-ordinate axis are `-2, 4/3, - 4/5`.
Concept: undefined >> undefined
The angle between the line `vecr = (5hati - hatj - 4hatk) + lambda(2hati - hatj + hatk)` and the plane `vec.(3hati - 4hatj - hatk)` + 5 = 0 is `sin^-1(5/(2sqrt(91)))`.
Concept: undefined >> undefined
The angle between the planes `vecr.(2hati - 3hatj + hatk)` = 1 and `vecr.(hati - hatj)` = 4 is `cos^-1((-5)/sqrt(58))`.
Concept: undefined >> undefined
The line `vecr = 2hati - 3hatj - hatk + lambda(hati - hatj + 2hatk)` lies in the plane `vecr.(3hati + hatj - hatk) + 2` = 0.
Concept: undefined >> undefined
The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is `vecr = (5hati - 4hatj + 6hatk) + lambda(3hati + 7hatj - 2hatk)`.
Concept: undefined >> undefined
If the foot of perpendicular drawn from the origin to a plane is (5, – 3, – 2), then the equation of plane is `vecr.(5hati - 3hatj - 2hatk)` = 38.
Concept: undefined >> undefined
Write the negation of the following simple statements.
The number 17 is prime.
Concept: undefined >> undefined
Write the negation of the following simple statements.
2 + 7 = 6.
Concept: undefined >> undefined
Write the negation of the following simple statements.
Violets are blue.
Concept: undefined >> undefined
Write the negation of the following simple statements.
`sqrt(5)` is a rational number.
Concept: undefined >> undefined
Write the negation of the following simple statements.
2 is not a prime number.
Concept: undefined >> undefined
Write the negation of the following simple statements.
Every real number is an irrational number.
Concept: undefined >> undefined
Write the negation of the following simple statements.
Cow has four legs.
Concept: undefined >> undefined
Write the negation of the following simple statements.
A leap year has 366 days.
Concept: undefined >> undefined
Write the negation of the following simple statements
All similar triangles are congruent.
Concept: undefined >> undefined
Write the negation of the following simple statements
A leap year has 366 days.
Concept: undefined >> undefined
Write the negation of the following simple statements
Area of a circle is same as the perimeter of the circle.
Concept: undefined >> undefined
