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MathsJEE Main 2 Apr 2026, Shift 1·Q15·MCQ·Moderate

3D Geometry · Foot of perpendicular to line

Let a line LL passing through the point (1,1,1)(1, 1, 1) be perpendicular to both the vectors 2i^+2j^+k^2\hat i + 2\hat j + \hat k and i^+2j^+2k^\hat i + 2\hat j + 2\hat k. If P(a,b,c)P(a, b, c) is the foot of perpendicular from the origin on the line LL, then the value of 34(a+b+c)34(a + b + c) is:
  1. (1)50
  2. (2)80
  3. (3)100
  4. (4)120
We corrected a printing error in the original paper

Source printed the second vector as “i^+2j^+k^\hat i + 2\hat j + \hat k”; corrected to the intended “i^+2j^+2k^\hat i + 2\hat j + 2\hat k” (the source's own solution uses it; as printed 34(a+b+c)=95.234(a+b+c) = 95.2, no option).

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