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701.

True and FalseIf \(\vec a\) and \(\vec b\) are adjacent sides of a rhombus, then \(\vec a . \vec b = 0.\)

Answer»

False

Explanation:

Given that, \(\vec a . \vec b = 0\) ⇒ \(\vec a \,and\, \vec b\) are perpendicular to each other.

But, adjacent sides of rhombus are not perpendicular.

702.

If θ be the angle between any two vectors a and b, then |a . b| = |a × b|, when θ is equal to(A) 0(B) π/4(C) π/2(D) π

Answer»

Correct answer is

(B) π/4

703.

If a and b are unit vectors, then what is the angle between a and b for √3a - b to be a unit vector ?(A) 30º (B) 45º (C) 60º (D) 90º

Answer»

Correct answer is

(A) 30º

704.

Two foreces `vecP and vecQ` are acting at a point . If `vecP` is reversed, the new resultant becomes between magnitudes of P and Q is given by `P = KQ `. Find k.

Answer» Correct Answer - 1
`vecR_(1) = vecQ + vecP` and `vecR_(2) = vecQ - vecP`
Given that `vecR_(1)` and `vecR_(2)` are perpendicular, therefore,
`vecR_(1) . vecR_(2) = 0`
`(vecQ + vecP).(vecQ- vecP) = 0`
`Q^(2) - P^(2) = 0`
`Q^(2) =P^(2)`
`Q^(2) = k^(2) Q^(2)`
`rArr" "k= 1`