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Find angle between the vectors overset(t...

Find angle between the vectors `overset(to)(a) = hat(i) + hat(j) - hat(k) and overset(to)(b) = hat(i) + hat(j) + hat(k)`

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The correct Answer is:
`theta = cos^(-1) ((1)/(3))`
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Find lambda if the vectors overset(to)(a) = hat(i) +3 hat(j) + hat(k) , overset(to)(b) = 2hat(i) - hat(j) - hat(k) and overset(to) (c ) = lambda hat(i) + 7 hat(j) + 3 hat(k) are coplanar

Find the angle between the vectors vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(i) - hat(j) + hat(k) .

Find the distance between the lines overset(to)(r ) = hat(i) + 2 hat(j) - 4 hat(k) + lambda ( 2 hat(i) + 3 hat(j) + 6 hat(j) ) & overset(to)(r ) = 3 hat(i) + 3 hat(j) - 5 hat(k) + mu ( -2 hat(i) + 3 hat(j) + 8 hat(k) )

Find the area of the parallelogram whose adjacent sides are determined by the vectors vec(a) = hat(i) - hat(j) + 3hat(k) and vec(b) = 2hat(i) - 7hat(j) + hat(k) .

Find the value of lambda if the vectors vec(a) = 3hat(i) + hat(j) - 2hat(k) and vec(b) = hat(i) + lambda hat(j) - 3hat(k) are perpendicular to each other.

Write a unit vector in the direction of the sum of vectors vec(a) = 2hat(i) - hat(j) + 2hat(k) and vec(b) = -hat(i) + hat(j) + 3hat(k) .

Write a unit vector in the direction of the sum of vectors vec(a) = 2hat(i) + 2hat(j) - 5hat(k) and vec(b) = 2hat(i) + hat(j) - 7hat(k) .

Write the value of lambda so that the vectors vec(a) = 2hat(i) + lambda hat(j) + hat(k) and vec(b) = hat(i) - 2hat(j) + 3hat(k) are perpendicular to each other ?

Obtain the projection of the vector vec(a) = 2hat(i) + 3hat(j) + 2hat(k) on the vector vec(b) = hat(i) + 2hat(j) + hat(k) .

Find the sine of the angle between the vectors hat(i) + 2 hat(j) + 2 hat(k) and 3 hat(i) + 2 hat(j) + 6 hat(k)

SUNSTAR PUBLICATION-ANNUAL EXAM QUESTION PAPER MARCH - 2016-PART - B (Answer any ten questions)
  1. Evaluate : int(0)^(pi) ( sin^(2) ((x)/(2) ) - cos^(2) ( (x)/(2) ))dx

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  2. If |overset(to)(a) + overset(to)(b)| =| overset(to)(a) - overset(to)(b...

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  3. Find the order and degree, if defined, of the differential equation. ...

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  4. Find angle between the vectors overset(to)(a) = hat(i) + hat(j) - hat(...

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  5. The random variable X has probability distribution P(X) of the followi...

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  6. Find the Cartesian equation of the line parallel to y - axis and passi...

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  7. Write the simplest form of tan^(-1) [( 3 cos x - 4 sin x )/( 4 cos x +...

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  8. Using determinants show that points A (a, b+ c) , B (b,c+ a) and C ( c...

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  9. If functions f : R to R and g: R to R are given by f(x) = |x| and g(x)...

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  10. Show that sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x, (1)/(sqrt2)le x le 1.

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  11. Find (dy)/(dx) if y= sec^(-1)((1)/(2x^(2)-1)), 0 lt x lt (1)/(sqrt(2))

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  12. If x^(y) = a^(x), prove that (dy)/( dx) = ( x log (e) a -y)/( x log(e)...

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  13. Find int (1)/( sin x cos^(3) x) dx

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  14. Using differentials find the approximate value of (25)^(1//3)

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  15. Evaluate : int(0)^(pi) ( sin^(2) ((x)/(2) ) - cos^(2) ( (x)/(2) ))dx

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  16. If |overset(to)(a) + overset(to)(b)| =| overset(to)(a) - overset(to)(b...

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  17. Find the order and degree, if defined, of the differential equation. ...

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  18. Find angle between the vectors overset(to)(a) = hat(i) + hat(j) - hat(...

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  19. The random variable X has probability distribution P(X) of the followi...

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  20. Find the Cartesian equation of the line parallel to y - axis and passi...

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    |