Question:
Let \(\mathbf{a} = \mathbf{i} - \mathbf{k}, \quad
\mathbf{b} = x\mathbf{i} + \mathbf{j} + (1-x)\mathbf{k}, \quad
\mathbf{c} = y\mathbf{i} + x\mathbf{j} + (1+x-y)\mathbf{k}\).
Then \([\mathbf{a}, \mathbf{b}, \mathbf{c}]\) depends on:
Let \(\mathbf{a} = \mathbf{i} - \mathbf{k}, \quad
\mathbf{b} = x\mathbf{i} + \mathbf{j} + (1-x)\mathbf{k}, \quad
\mathbf{c} = y\mathbf{i} + x\mathbf{j} + (1+x-y)\mathbf{k}\).
Then \([\mathbf{a}, \mathbf{b}, \mathbf{c}]\) depends on:
Show Hint
Check cancellation in determinants before concluding dependence.
Updated On: Mar 23, 2026
- only y
- only x
- both x and y
- neither x nor y
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Compute scalar triple product as determinant.
Step 2: On expansion, all x,y terms cancel, leaving a constant.
Was this answer helpful?
0
0
Top BITSAT Mathematics Questions
- The solution of $\sin^{-1}\,x-\sin^{-1}\,2x=\pm\frac{\pi}{3}$ is
- If one root of the quadratic equation $a x^{2}+b x+c=0$ is equal to $n^{\text {th }}$ power of the other root, then the value of: $a^{\frac{n}{n-1}} C^{\frac{1}{n-1}}+c^{\frac{n}{n-1}} a^{\frac{1}{n-1}}$ is equal to
- $(x -1) (x^2 - 5x + 7) < (x -,1),$ then $x$ belongs to
- An ellipse has $OB$ as semi-minor axis, $F$ and $F$ are its foci and the $\angle FBF$, is a right angle. Then, the eccentricity of the ellipse is
- $2^{1/4}. 2^{2/8}. 2^{3/16}. 2^{4/32}......\infty$ is equal to-
View More Questions
Top BITSAT Vector basics Questions
- If \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k} \) and \( \vec{b} = 2\hat{i} - \hat{j} + 2\hat{k} \), then find the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \).
- If the midpoints of sides BC, CA, AB of triangle ABC are respectively D, E, F, then position vector of centre of triangle DEF, when position vectors of A, B, C are respectively i+ j, j+ k, k+ i, is
- Let a, b, c be three vectors satisfying a × b = ( a × c), | a|=| c|=1, | b|=4 and | b × c|=√(15). If a · b = ?, then λ equals
- If i+ j, j+ k, i+ k are position vectors of vertices of triangle ABC taken in order, then ∠ A is equal to:
- The projection of the line joining (3,4,5) and (4,6,3) on the line joining (-1,2,4) and (1,0,5) is:
View More Questions
Top BITSAT Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?
View More Questions