Advertisements
Advertisements
Question
Two vectors `veca = a_1 hati + a_2 hatj + a_3 hatk` and `vecb = b_1 hati + b_2 hatj + b_3 hatk` are collinear if ______.
Options
a1b1 + a2b2 + a3b3 = 0
`a_1/b_1 = a_2/b_2 = a_3/b_3`
a1 = b1, a2 = b2, a3 = b3
a1 + a2 + a3 = b1 + b2 + b3
Advertisements
Solution
Two vectors `veca = a_1 hati + a_2 hatj + a_3 hatk` and `vecb = b_1 hati + b_2 hatj + b_3 hatk` are collinear if `underlinebb(a_1/b_1 = a_2/b_2 = a_3/b_3)`.
RELATED QUESTIONS
Write the number of vectors of unit length perpendicular to both the vectors `veca=2hati+hatj+2hatk and vecb=hatj+hatk`
For given vectors, `veca = 2hati - hatj + 2hatk` and `vecb = -hati + hatj - hatk`, find the unit vector in the direction of the vector `veca +vecb`.
Identify the unit vector in the following.
How do you deduce that two vectors are perpendicular?
The position vector particle has a length of 1m and makes 30° with the x-axis. What are the lengths of the x and y components of the position vector?
Compare the components for the following vector equations
(a) `"T"hatj - "mg"hatj = "ma"hatj`
(b) `vecT + vecF = vecA + vecB`
(c) `vecT - vecF = vecA - vecB`
(d) `"T"hatj + "mg"hatj = "ma"hatj`
If the horizontal and vertical components of a force are negative, then that force is acting in between
If a line makes angles 120° and 60° with the positive directions of X and Z axes respectively then the angle made by the line with positive Y-axis is ______.
If `veca = 4hati + 6hatj` and `vecb = 3hatj + 4hatk`, then the vector form of the component of `veca` along `vecb` is ______.
Check whether the vectors `2hati +2hatj +3hatk,-3hati +3hatj +2hatk and 3hati + 4hatk` From a triangle or not.
Check whether the vectors `2hati + 2hatj+ 3hatk`, `-3hati + 3hatj +2hatk` and `3hati + 4hatk` form a triangle or not.
If `veca = 3hati - 2hatj + hatk` and `vecb = 2hati - 4hatj - 3hatk` then the value of `|veca - 2vecb|` will be ______.
Shown below is a cuboid. Find `vec(BA).vec(BC)`.
If \[P(x,y,z)\] is a point, what is its position vector?
For \[\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}\], which quantities are called the components of \[\vec{a}\]?
If \[\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}\] and \[\vec{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}\], what is \[\vec{a}+\vec{b}\]?
If \[\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}\] and \[\vec{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}\], what is \[\vec{a}-\vec{b}\]?
Which expression represents scalar multiplication of \[\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}\] by \[\lambda\]?
When are two vectors equal?
When are two vectors collinear?
What is the magnitude of \[\vec{a}=\vec{i}-2\vec{j}\]?
What is the unit vector in the same direction as \[\vec{a}=\vec{i}-2\vec{j}\]?
Which vector has magnitude \[7\] units in the direction of \[\vec{a}=\vec{i}-2\vec{j}\]?
