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Find the value of 'lambda' if the plane...

Find the value of `'lambda'` if the planes `vecr. (hati +2hatj+3hatk)+3=0` and `vecr. (lambdahati+2hatj+7hatk) = 10` are perpendicular.

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Here `vecn_(1) = hati+2hatj+3hatk`
and `vecn_(2) = lambdahati+2hatj-7hatk`
For perpendicular planes
` vecn_(1).vecn_(2) = 0`
`rArr (hati+2hatj+3hatk).(lambdahati+2hatj-7hatk)=0`
`rArr lambda +4 - 21 = 0`
`rArr lambda = 17`.
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NAGEEN PRAKASHAN ENGLISH-THREE-DIMENSIONAL GEOMETRY -Miscellaneous Exercise
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  2. Show that the line joining the origin to the point (2,1,1) is perpe...

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  3. If l(1), m(1), n(1) and l(2),m(2),n(2) are the direction cosines of tw...

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  4. Find the angle between the lines whose direction ratios are a, b, c a...

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  5. Find the equation of a line parallel to x-axis and passing through ...

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  6. If the coordinates of the points A ,B ,C ,D are (1,2,3),(4,5,7),(-4,3,...

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  7. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2and (x-1)/(3k)=(y-1)/1=(z-6...

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  8. Find the vector equation of the line passing through (1, 2, 3) and ...

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  9. Write the vector equation of the plane, passing through the point (a ,...

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  10. Find the shortest distance between lines vecr = 6hati+2hatj+2hatk+lam...

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  11. Find the coordinate of the point where the line through (5, 1, 6) and ...

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  12. Find the coordinates of the point where the line through (5, 1, 6) ...

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  13. Find the coordinates of the point where the line through (3, -4, -5...

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  14. Find the equation of the plane passing through the point (-1, 3, 2)...

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  15. If the points (1," "1," "p)" "a n d" "(" "3," "0," "1) be equidistant ...

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  16. Find the equation of the plane passing through the line of intersectio...

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  17. If O be the origin and the coordinates of P be(1," "2," "" "3) , th...

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  18. Find the equation of the plane which contains the line of intersection...

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  19. Find the distance of the point (-1,-5,-10) from the point of the inter...

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  20. Find the vector equation o the line passing through (1,2,3) and parall...

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  21. Find the vector equation of line passing through the point (1, 2, -4) ...

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