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If OP=8 and OP makes angles 45^(@) and 6...

If OP=8 and OP makes angles `45^(@) and 60^(@)` with OX-axis and OY-axis respectively, then OP is equal to

A

`8(sqrt(2)hati+hatj+-hatk)`

B

`4(sqrt(2)hati+hatj+-hatk)`

C

`(1)/(4)(sqrt(2)hati+hatj+-hatk)`

D

`(1)/(8)(sqrt(2)hati+hatj+-hatk)`

Text Solution

Verified by Experts

The correct Answer is:
B
Here is the only vector `4(sqrt(2)hati+hatj+-hatk)`, whose length is 8.
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ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
  1. In the figure, a vectors x satisfies the equation x-w=v. then, x is eq...

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  2. Vectors veca = hati+2hatj+3hatk, vec b = 2hati-hatj+hatk and vecc= 3ha...

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  3. If OP=8 and OP makes angles 45^(@) and 60^(@) with OX-axis and OY-axis...

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  4. Let a,b and c be three unit vectors such that 3a+4b+5c=0. Then which o...

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  5. if A,B,C,D and E are five coplanar points, then vec(DA) + vec( DB) + v...

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  6. If the vectors veca and vecb are linearly independent satisfying (sqrt...

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  7. Find the slope of the normal having point (3,2) and (4,1)

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  8. A line passes through the points whose position vectors are hati+hatj-...

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  9. Find the slop of line . The Equation of line is 2x-3y=2

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  10. If P and Q are the middle points of the sides BC and CD of the paralle...

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  11. If the figure formed by the four points hati+hatj-hatk,2hati+3hatj,3ha...

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  12. A and B are two points. The position vector of A is 6b-2a. A point P ...

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  13. If three points A,B and C are collinear, whose position vectors are ha...

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  14. If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC res...

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  15. The two adjacent sides of a parallelogram are 2hati+4hatj-5hatk and ha...

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  16. If A,B and C are the vertices of a triangle with position vectors vec(...

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  17. If ABCDEF is a regular hexagon then vec(AD)+vec(EB)+vec(FC) equals :

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  18. Find the discriminant of the quadratic equation x^2+3x+2

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  19. In a regular hexagon ABCDEF, prove that AB+AC+AD+AE+AF=3AD.

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  20. Find the dot product of the vector 2hati+3hatj+1hatk and 1hati+2hatj+3...

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